rhiever/Rmagic demo

## Rmagic demo
{
 "metadata": {
  "name": "Introduction to Linear Models"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# ZOL851 Intro tutorial on GLM in R\n",
      "\n",
      "Ian Dworkin\n",
      "\n",
      "September 18, 2012\n",
      "\n",
      "In this tutorial we are going to examine how **R** \f",
      "fits some simple linear models,\n",
      "and how we can interpret some of the outputs. I generally like to call all of the\n",
      "libraries that I will use \f",
      "first, and double check that there are no conflicts (in\n",
      "terms of names of functions)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%load_ext rmagic"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 87
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "# changes some default display options\n",
      "options(show.signif.stars=F)\n",
      "options(digits=3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 88
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "require(arm)\n",
      "require(car)\n",
      "require(lattice)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 89
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Reading in & and checking the data\n",
      "\n",
      "As usual, we set our working directory and read in the data. You will want to\n",
      "change the working directory to your home directory."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -nd dll.data\n",
      "dll.data <- read.csv(\"/Users/olsonran/Documents/dll.csv\", header=TRUE)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 90
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I always start by looking at the input of the data \f",
      "rst using `summary(your.data.frame)`\n",
      "and `str(your.data.frame)`. I also use `head(your.data.frame)` and `tail(your.data.frame)`\n",
      "to con\f",
      "rm it was all imported as expected. For space here, I will not call them\n",
      "but you should run them yourself `summary(dll.data)`, `str(dll.data)`, etc...\n",
      "\n",
      "If you have used these functions, you will see that some of the variable in\n",
      "`dll.data` are treated numerically, when in fact we want them to be treated\n",
      "as factors. In particular temp and replicate. So we have **R** change these to\n",
      "factors."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "dll.data$temp <- factor(dll.data$temp)\n",
      "dll.data$replicate <- factor(dll.data$replicate)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 91
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We also want to make sure that the default level of the factor `genotype==\"wt\"`.\n",
      "By default factors in **R** go alpha-numerically. That is the lowest letter of the\n",
      "alphabet, or smallest numbers are the default base level. However, we want to\n",
      "reset this to aid in intepretation. To do this we use the relevel function, which\n",
      "has the name of the variable that we are changing, and the new default level"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "dll.data$genotype <- relevel(dll.data$genotype, \"wt\")  \n",
      " # Setting the wild-type (wt) as reference"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 92
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For the purposes of this tutorial we are also going to remove all rows that\n",
      "have any missing observations. This is not generally advisable, and the smarter\n",
      "approach would be to just remove speci\f",
      "c rows that have missingness for the\n",
      "variables used in the model."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "dll.data <- na.omit(dll.data) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 93
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "At this point it is wise to call `summary()` and `str()` for your data frame\n",
      "again to make sure the expected changes occurred.\n",
      "\n",
      "# Some quick data exploration\n",
      "\n",
      "Before we \f",
      "fit the models, we will quickly do some exploratory plots. Please\n",
      "review the exploratory data analysis tutorial for more details."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "# The plot\n",
      "plot(dll.data$SCT ~ dll.data$tarsus, \n",
      "      col=c(\"red\", \"blue\")[dll.data$genotype], ylim=c(5,25), \n",
      "      pch=c(1,2)[dll.data$temp],cex=0.8, ylab=\"# of SCT\", \n",
      "      xlab=\"Tarsus length\", \n",
      "      main=\"scatterplot of Sex comb teeth and basi tarsus length\")\n",
      "\n",
      "# Add a legend    \n",
      "legend(0.23,25, legend=c(\"Dll 25\",\"Dll 30\", \"wt 25\", \"wt 30\"),\n",
      "      col=c(\"red\", \"red\", \"blue\", \"blue\"), pch=c(1,2,1,2))\n",
      "\n",
      "# lowess curves\n",
      "lines(lowess(dll.data$tarsus[dll.data$genotype==\"Dll\" & dll.data$temp==\"25\"],\n",
      "     dll.data$SCT[dll.data$genotype==\"Dll\" & dll.data$temp==\"25\"]), \n",
      "     lwd=2, type=\"o\", col=\"red\")\n",
      "\n",
      "lines(lowess(dll.data$tarsus[dll.data$genotype==\"Dll\" & dll.data$temp==\"30\"],\n",
      "     dll.data$SCT[dll.data$genotype==\"Dll\" & dll.data$temp==\"30\"]), \n",
      "     lwd=2, type=\"o\", col=\"red\", pch=2) \n",
      "\n",
      "lines(lowess(dll.data$tarsus[dll.data$genotype==\"wt\" & dll.data$temp==\"25\"],\n",
      "     dll.data$SCT[dll.data$genotype==\"wt\" & dll.data$temp==\"25\"]), \n",
      "     lwd=2, type=\"o\", col=\"blue\")\n",
      "\n",
      "lines(lowess(dll.data$tarsus[dll.data$genotype==\"wt\" & dll.data$temp==\"30\"],\n",
      "     dll.data$SCT[dll.data$genotype==\"wt\" & dll.data$temp==\"30\"]), \n",
      "     lwd=2, type=\"o\", col=\"blue\", pch=2) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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UMAE//fTT+PLLL3H11Vfj/fffR4UKFSzTyZMn2+2fffZZsow5aYt/weS7774D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BL5DPm8BifWLYC42GPXM+GNQQQyx9NPHisr5L0L6QP2CeBC/jIvt+ZEYC5d+s+7klU5AswtQteb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\nQAREIFoI/D+lWm0G6iNoFwAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 94
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this case, the lowess lines are not actually very informative on the plot,\n",
      "but perhaps we can see the di\u000b",
      "erence in the trend for the relationship between\n",
      "`SCT` and `tarsus` across the two genotypes.\n",
      "\n",
      "We could do a fair bit of additional plotting, but I leave this as an exercise\n",
      "(see associated **R** code).\n",
      "\n",
      "# using the lm() function in R\n",
      "\n",
      "To perform this regression in **R** we use the `lm()` function. lm stands for Linear\n",
      "Model. As we will learn linear regression is just a special case of the *general\n",
      "linear model* in statistics.\n",
      "\n",
      "In **R** we regress `y` onto `x` like:\n",
      "\n",
      "`lm(y \u0018~ x, data=YourData)`, where the tilde ('~') means 'is modeled as'.\n",
      "\n",
      "So you would read this as \"y is modeled as a function of x\". Using the `lm()`\n",
      "additionally implies that we are assuming that the residual (unexplained) variation\n",
      "in the model is normally distributed, and that the response is (to a \f",
      "rst\n",
      "approximation) a continuous variable. So we are really \f",
      "fitting the model.\n",
      "\n",
      "$y = f(x) ~ N(\\beta_0 + \\beta_1x, \\sigma)$ , where\n",
      "\n",
      "$N()$ means normally distributed with mean (\u0016$\\mu$) equal to $\\beta_0 + \\beta_1x$\n",
      "\n",
      "$\\beta_0$ is the intercept\n",
      "\n",
      "$\\beta_1$ is the slope of the regression line\n",
      "\n",
      "$\\sigma$ is the distribution for the residual (unexplained) variation. The variation\n",
      "remaining in our response ($y$) after accounting for the model. Here I have it in\n",
      "the same units as $y$, but you will often see it expressed as a variance ($\\sigma^2$), and\n",
      "being labeled the unexplained variance of the model.\n",
      "\n",
      "Using the `lm()` in **R** assumes that you want to fi\f",
      "t an intercept term in your\n",
      "model (which we almost want to do). So we did not need to explicitly include\n",
      "it in the function call to `lm()`. However, we certainly can (and it is probably a\n",
      "good idea when you are \f",
      "rst starting out). In any case it means that these two\n",
      "calls are equivalent:\n",
      "\n",
      "$lm(y ~ 1 + x)$\n",
      "\n",
      "$lm(y ~ x)$\n",
      "\n",
      "Now we actually \f",
      "fit the model in **R**."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "regression.1 <- lm(SCT ~ tarsus, data=dll.data) # The intercept is implicit\n",
      "regression.1.Intercept <- lm(SCT ~ 1 + tarsus, data=dll.data) \n",
      "  # With explicit intercept, but the same as above!"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 95
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It is useful to remind ourselves of the design matrix. We can use the\n",
      "`model.matrix()`. Remember that it will have as many rows as observations!\n",
      "We will just look at the \f",
      "first few observations."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(head(model.matrix(regression.1)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "  (Intercept) tarsus\n",
        "1           1  0.219\n",
        "2           1  0.214\n",
        "3           1  0.211\n",
        "5           1  0.207\n",
        "6           1  0.207\n",
        "7           1  0.204\n"
       ]
      }
     ],
     "prompt_number": 96
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is just a matrix so we can use indexing like normal in **R**."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(model.matrix(regression.1)[500:508,])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "    (Intercept) tarsus\n",
        "520           1  0.200\n",
        "521           1  0.199\n",
        "522           1  0.199\n",
        "523           1  0.198\n",
        "524           1  0.196\n",
        "525           1  0.196\n",
        "526           1  0.195\n",
        "527           1  0.194\n",
        "528           1  0.190\n"
       ]
      }
     ],
     "prompt_number": 97
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# INTERPRETING THE MODEL OUTPUT\n",
      "\n",
      "Let us fi\f",
      "rst look at the estimated coe\u000ecients from this regression. We use the\n",
      "`coef()` function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(coef(regression.1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "(Intercept)      tarsus \n",
        "       6.08       26.92 \n"
       ]
      }
     ],
     "prompt_number": 98
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "These represent the intercept and the slope of the model. However (and\n",
      "we will return to this), the intercept tells us the expected number of `SCT` when\n",
      "`tarsus=0`, which is clearly not a sensible value. The tarsus could not have a\n",
      "zero length, and how could sex comb teeth be present on a structure with a zero\n",
      "length?\n",
      "\n",
      "We should also look at the confi\f",
      "dence intervals for our estimated slope and\n",
      "intercept. There is a handy function `confint()` to get the 95% con\f",
      "dence\n",
      "intervals for these parameters."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(confint(regression.1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "            2.5 % 97.5 %\n",
        "(Intercept)  5.35   6.82\n",
        "tarsus      23.02  30.81\n"
       ]
      }
     ],
     "prompt_number": 99
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "One thing that is clear from these values, the 95% CI do not overlap with\n",
      "zero, consistent with a so-called 'statistically signi\f",
      "cant' eff\u000b",
      "ect.\n",
      "\n",
      "As we often do with **R**, we will use the `summary()` function. However before\n",
      "we do for the linear model, I want to make a slight detour for a discussion\n",
      "about generic functions in **R**. When you call `summary()`, the \f",
      "rst thing it does\n",
      "is look at the class of the object, and then it uses a class speci\f",
      "c method. What\n",
      "this means is that calling `summary()` actually calls di\u000b",
      "fferent functions depending\n",
      "upon the class of the object.\n",
      "\n",
      "If you look up the help for `summary()`, `?summary` under the description it\n",
      "will say \"summary is a generic function used to produce result summaries of\n",
      "the results of various model \f",
      "tting functions. The function invokes particular\n",
      "methods which depend on the class of the fi\f",
      "rst argument.\" What this means\n",
      "is that if you call `summary()` on a data frame, i.e. `summary(your.data)`, it\n",
      "is actually calling the function `summary.data.frame(your.data)`. If you call\n",
      "`summary(your.model.object)` on a linear model object, `lm(your.model)`, it\n",
      "will actually call the function `summary.lm(your.model.object)`. To get a better\n",
      "sense of this type `methods(summary)` into the **R** console, and you will see a\n",
      "list of di\u000b",
      "fferent class specifi\f",
      "c methods for the `summary()` generic function. This\n",
      "is why summary seems to do so many di\u000b",
      "fferent things!!! It also means if you\n",
      "want to understand more about `summary.lm` you need to use `?summary.lm`.\n",
      "\n",
      "Now back to the linear model."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(summary(regression.1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "\n",
        "Call:\n",
        "lm(formula = SCT ~ tarsus, data = dll.data)\n",
        "\n",
        "Residuals:\n",
        "   Min     1Q Median     3Q    Max \n",
        "-4.633 -1.012 -0.123  0.845 11.226 \n",
        "\n",
        "Coefficients:\n",
        "            Estimate Std. Error t value Pr(>|t|)\n",
        "(Intercept)    6.083      0.374    16.2   <2e-16\n",
        "tarsus        26.915      1.987    13.6   <2e-16\n",
        "\n",
        "Residual standard error: 1.55 on 1916 degrees of freedom\n",
        "Multiple R-squared: 0.0874,\tAdjusted R-squared: 0.0869 \n",
        "F-statistic:  184 on 1 and 1916 DF,  p-value: <2e-16 \n",
        "\n"
       ]
      }
     ],
     "prompt_number": 100
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There are a couple of useful aspects to this output. In addition to the\n",
      "estimated coeffi\u000ecients for the slope and intercept, we have their standard errors,\n",
      "t-values (which is just the parameter estimate divided by the standard error)\n",
      "and p-values. We can double the standard errors to get approximate con\f",
      "dence\n",
      "intervals but the `confint()` allows us to get these anyways. We also get the\n",
      "quantiles for the residuals. We expect that these should be symmetric in value,\n",
      "with the median close to zero. That is clearly not the case here, so we may want\n",
      "to look further at the residuals (which we will do in a later tutorial).\n",
      "\n",
      "$R^2$, also known as the coeffi\u000ecient of determination provides a quantitative\n",
      "assessment of *How much of the observed variation in our response (SCT) can\n",
      "be accounted for by our model?* In this case it is approximately 8%. While this\n",
      "is small, for a single variable such as a measure of length, that is not negligible\n",
      "by any means.\n",
      "\n",
      "It is also worth interpreting the Residual Standard Error (RSE). The RSE\n",
      "of the model is \u0018~ 1:55, which tells us we can predict the number of SCT on\n",
      "an individual with an accuracy of \u0018 1:55 SCT *given this model*. See page 41 of\n",
      "Gelman and Hill for more discussion.\n",
      "\n",
      "I also think it is generally wise to take a look at the co-variances for the\n",
      "estimated parameters. I am not speaking of co-variation or correlation of the\n",
      "observed values, but of the estimates we just produced for the slope and intercept.\n",
      "These helps you recognize whether the estimated values depend on each\n",
      "other (and suggests some lack of independence between predictors, or other\n",
      "issues in your model that need to be \f",
      "fixed)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(vcov(regression.1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "            (Intercept) tarsus\n",
        "(Intercept)        0.14  -0.74\n",
        "tarsus            -0.74   3.95\n"
       ]
      }
     ],
     "prompt_number": 101
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Question: How would we get the Standard errors for the estimates from this\n",
      "matrix? I will ask this in class.\n",
      "\n",
      "To address the degree of co-variation between the estimated slope and intercept,\n",
      "we look at the off\u000b",
      "-diagonals. Sometimes these are diffi\u000ecult to interpret\n",
      "as co-variances, so we convert this to a correlation matrix using the `cov2cor()`\n",
      "function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(cov2cor(vcov(regression.1)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "            (Intercept) tarsus\n",
        "(Intercept)       1.000 -0.995\n",
        "tarsus           -0.995  1.000\n"
       ]
      }
     ],
     "prompt_number": 102
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The diagonals are correlations of a parameter estimate on itself, so these\n",
      "have to be one, and are not interesting. We are again focused on the o\u000b",
      "ff-diagonal\n",
      "elements. In this case the value is \u0018$\\sim - .99$ which means that our parameter\n",
      "estimates are almost perfectly negatively correlated. This is clearly not good\n",
      "news. This problem is due almost entirely to the fact that we are estimating an\n",
      "intercept way outside the range of our data.\n",
      "\n",
      "Let's take a look at the estimated parameters again.\u0000"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(coef(regression.1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "(Intercept)      tarsus \n",
        "       6.08       26.92 \n"
       ]
      }
     ],
     "prompt_number": 103
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The intercept 6.08 is interpreted as the number of `SCT` when `tarsus=0`. This\n",
      "is clearly a very silly interpretation, inflates the SE for the intercept, and the\n",
      "co-variation between parameters. This plot demonstrates how crazy this would\n",
      "be. The **R** code for this (including con\f",
      "fidence intervals) is in the .R fi\f",
      "le of the\n",
      "same name with some comments to explain what we have done."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "plot(SCT ~ tarsus, data=dll.data, xlim=c(0, 0.258))\n",
      "abline(regression.1)\n",
      "\n",
      "# We can look at the confidence region (confidence bands ) as well to see how this influences our uncertainty.\n",
      "\n",
      "# To make confidence bands, we generally need to generate a set of \"new\" values for our explanatory variable (tarsus), and then use these to predict fitted values (and Confidence intervals on fitted values)\n",
      "\n",
      "# We make the range go from 0, since we are fitting the intercept back to zero.  Clearly a crazy idea!\n",
      "\n",
      "# make a new data frame with our \"new\" values of tarsus length\n",
      "new_tarsus <- data.frame(tarsus = seq(0, range(dll.data$tarsus)[2], by=0.005) )   # Makes a new data frame\n",
      "\n",
      "# \"predict\" values for our new values of tarsus\n",
      "predicted.model.1  <- predict(regression.1, new_tarsus, interval=\"confidence\")\n",
      "\n",
      "#Then we add these lines back on\n",
      "lines(x = new_tarsus[,1], y = predicted.model.1[,1], lwd=4) # this would be the same as abline(model.1)\n",
      "lines(x = new_tarsus[,1], y = predicted.model.1[,3], lwd=3, lty=2, col=\"grey\")\n",
      "lines(x = new_tarsus[,1], y = predicted.model.1[,2], lwd=3, lty=2, col = \"grey\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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PDi+88EK48MILw4477lj5ja+hFlaEAGaOFxP0D3/4w8B88Nprrx222267MHPmzBq6Feqq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\n91h5jOAAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 104
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Clearly we are estimating well outside the range of the observed data, including\n",
      "the con\f",
      "fidence bands around the best \f",
      "fit line. We can also look at a plot in\n",
      "parameter space (the previous plot was in the observation space). We do so by\n",
      "looking at the confi\f",
      "dence ellipse around the estimated parameters (slope and\n",
      "intercept)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "confidenceEllipse(regression.1)  \n",
      "    # The estimates are highly correlated with one another."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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cq/eGg1ncmXe0c1ZUJTpnBRM2ZZMACYScAA1wyIcgvBsgHnwA1vZNOlTlNcjZ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\nbmEAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 105
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This makes it very clear how much the parameter estimates for slope and\n",
      "intercept depend upon each other. If we decrease (by slight changes in the data\n",
      "or estimation procedure) the estimate of the slope, we get a pretty substantial\n",
      "increase in the intercept. So what do we do?\n",
      "\n",
      "#Interpreting coe\u000ecients: Sometimes we need to center the covariates\n",
      "\n",
      "Proper interpretation of the parameters of a model is the most important part\n",
      "of the inferential process (at least once you have a model to \f",
      "fit). This is what\n",
      "allows us to turn a hum drum statistical analysis into Biological inference!!!!\n",
      "However, often the \"default\" way we code our data and our analyses does not\n",
      "allow for easy interpretation. In this next part we are going to consider some\n",
      "simple things to make it easier to interpret our data.\n",
      "\n",
      "Not only is the intercept uninterpretable, but the CI's are really big at the\n",
      "intercept when `tarsus=0`. The fact that we are trying to estimate a parameter\n",
      "WAY OUTSIDE the range of our data is causing the highly inflated SE, and the\n",
      "covariance between parameter estimates. As we discussed in class, one simple\n",
      "way of dealing this is to center the covariates (in this case, just tarsus length),\n",
      "to help interpretability of the intercept. This will (as we will see) also get rid\n",
      "of the correlation between parameter estimates and the inflated standard error\n",
      "for the intercept. So let's center the data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "dll.data$cent.tarsus <- dll.data$tarsus - mean(dll.data$tarsus)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 106
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You can also use the `scale(your.x, center=T, scale=F)`. If you keep\n",
      "`scale=T`, then it will also rescale the variable by its standard deviation (which\n",
      "we do not want at the moment)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "par(mfrow=c(2,1))\n",
      "hist(dll.data$tarsus, breaks=15)\n",
      "hist(dll.data$cent.tarsus, breaks=15) #just changes the mean"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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+/HifZVyxYoVkzpzZZ5xADprLkFq3bp0kenKWIaEsVuW56aab9AM9kmTAHSQQ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\n"
      }
     ],
     "prompt_number": 107
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The mean changes as we expect."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(mean(dll.data$tarsus))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "[1] 0.188\n"
       ]
      }
     ],
     "prompt_number": 108
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(mean(dll.data$cent.tarsus))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "[1] 2.06e-18\n"
       ]
      }
     ],
     "prompt_number": 109
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "However the standard deviation does not change."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(sd(dll.data$tarsus))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "[1] 0.0179\n"
       ]
      }
     ],
     "prompt_number": 110
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(sd(dll.data$cent.tarsus))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "[1] 0.0179\n"
       ]
      }
     ],
     "prompt_number": 111
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We now re-run the model with the centered co-variate."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "regression.2 <-lm(SCT ~ cent.tarsus, data=dll.data)\n",
      "\n",
      "par(mfrow=c(2,1))\n",
      "plot(SCT~cent.tarsus,data=dll.data, cex=0.5, pch=16)\n",
      "abline(regression.2)\n",
      "\n",
      "new_tarsus.2 <- data.frame(cent.tarsus = seq(range(dll.data$cent.tarsus)[1], range(dll.data$cent.tarsus)[2], by=0.005) )   # Makes a new data frame\n",
      "\n",
      "# \"predict\" values for our new values of tarsus\n",
      "predicted.model.2 <- predict(regression.2, new_tarsus.2, interval=\"confidence\")\n",
      "\n",
      "#Then we add these lines back on\n",
      "lines(x = new_tarsus.2[,1], y = predicted.model.2[,1], lwd=3) # this would be the same as abline(model.1)\n",
      "lines(x = new_tarsus.2[,1], y = predicted.model.2[,3], lwd=2, lty=2)\n",
      "lines(x = new_tarsus.2[,1], y = predicted.model.2[,2], lwd=2, lty=2)\n",
      "\n",
      "confidenceEllipse(regression.2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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DIc5vzjXDDBsWrmXUqFGhXJQTPwPMvIbvZM5D+8dzhEU5FudYSqMaxgIan/X/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\nBEjg/wHTNVyKElwpvwAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 112
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that we are estimating within the range of our data now. We\n",
      "can also see that the correlation between the parameter estimates is ~\u0018 0."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(cov2cor(vcov(regression.2)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "            (Intercept) cent.tarsus\n",
        "(Intercept)     1.0e+00    -5.5e-16\n",
        "cent.tarsus    -5.5e-16     1.0e+00\n"
       ]
      }
     ],
     "prompt_number": 113
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So how do we interpret the coe\u000efficients with the centered data? First o\u000b",
      ", you\n",
      "will notice that only the estimate of the intercept and its standard error have\n",
      "changed for this model."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(summary(regression.2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "\n",
        "Call:\n",
        "lm(formula = SCT ~ cent.tarsus, data = dll.data)\n",
        "\n",
        "Residuals:\n",
        "   Min     1Q Median     3Q    Max \n",
        "-4.633 -1.012 -0.123  0.845 11.226 \n",
        "\n",
        "Coefficients:\n",
        "            Estimate Std. Error t value Pr(>|t|)\n",
        "(Intercept)  11.1324     0.0355   313.6   <2e-16\n",
        "cent.tarsus  26.9151     1.9867    13.6   <2e-16\n",
        "\n",
        "Residual standard error: 1.55 on 1916 degrees of freedom\n",
        "Multiple R-squared: 0.0874,\tAdjusted R-squared: 0.0869 \n",
        "F-statistic:  184 on 1 and 1916 DF,  p-value: <2e-16 \n",
        "\n"
       ]
      }
     ],
     "prompt_number": 114
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The intercept now tells us what the expected number of `SCT` is when tarsus\n",
      "is at its mean, i.e. 11.1. You can also see that the standard error associated\n",
      "with the intercept is much smaller.\n",
      "\n",
      "We can use the `coefplot()` in the arm library to take a quick look at our\n",
      "estimates. The thick error bars represent one standard error, and the thinner\n",
      "bars are 2$\\times$ standard errors."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "coefplot(regression.2, intercept=T, vertical=F, ylim=c(0, 35)) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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L9PrtMvrT3s7e56nOt/5iZN0/Nlcl9JcW6xaDuSphfdTKec0Urp95BMpCgAAuC2X24auA\nXn7Wj+3oZH02VHbt2mXmddSt9nT79u0rL774oujHZbS3Z/fcevToYcrpCObrrrtOrIFdUjxstYD9\nZm8KW//oJVudtDelo6T1sqyO0NVem06vvfaaWPdQzSVt3Zf23HSyLwmfar0pXOgfvXytl251BK/u\nW0doWwOKzHFpUEU6TZ8+XfSXiuKPb775xvwCofu3PpNser56idga+GWcrMFMZtf25WC9TF/8knhp\njk0v5+tIamuwmxnBbn3WV2bOnGmq0mU62fvU3rheWdAp3PnW8NdR13pbwBpAJlutj03pCHWd9Bc1\nJgSiImD9xsmEQMwI2IOwCo+C1oO37ucFWrVqZQbmWB9nMe3RwUg68MoKVbPc+rhQwB7kYzdYB/Ho\n4CArHANWLy+go4it/4hmxLI9ClpHOBefrN6sGdSjZXVk8K9+9StnRLIO+NIBTvbgJC1jBX/A+jiN\nqeZU64sPYtKNrI9GBax7r86AMz1eK+ycw7IHYRUehKajjnXfVpA65QrPhBuEpdtZ3zhmik+dOjXQ\nunVrMxJal1v3TANW8DlVqZsVcGZf1iX2kKOgH330UWcbHRCldVk9U7NMz4s+1+110gFx9khl6+NU\nzsA3+8tJsrOzA9bVD7ONnledTnW+rV57wLqcbQbu6b70daGD63SAFhMC0RBI0p1aL0YmBOJWQHvB\n+llW/Txv4UkvXWvvtkOHDk4vSO8F6qVovbesX295qmnnzp3mPmaoS796CVUHCtk9tuL1nWp98fJ6\nKVUv0dr3Touv9/O5DubSS7a67+KXk3WdXg4ufA860mPRtya9elD8vNn16iAq7ZHrQLHCVylCnW97\nO12v500HX+l4ACYEoiVAAEdLnv1GXUDvzeq3aeklSL1Mrfd/rd6nWL090fu6TAgggICfAgSwn7rU\nXa4FtDc5ePBgM8pXe8g6oEt7w88884z5xqVyffAcHAIIxLwAARzzp5AGeCGgo6ELX8b0ok7qQAAB\nBMIJEMDhdFiHAAIIIICATwJ8DMknWKpFAAEEEEAgnAABHE6HdQgggAACCPgkQAD7BEu1CCCAAAII\nhBMggMPpsA4BBBBAAAGfBAhgn2CpFgEEEEAAgXACBHA4HdYhgAACCCDgkwAB7BMs1SKAAAIIIBBO\ngAAOp8M6BBBAAAEEfBIggH2CpVoEEEAAAQTCCRDA4XRYhwACCCCAgE8CBLBPsFSLAAIIIIBAOAEC\nOJwO6xBAAAEEEPBJgAD2CZZqEUAAAQQQCCdAAIfTYR0CCCCAAAI+CRDAPsFSLQIIIIAAAuEECOBw\nOqxDAAEEEEDAJwEC2CdYqkUAAQQQQCCcAAEcTod1CCCAAAII+CRAAPsES7UIIIAAAgiEEyCAw+mw\nDgEEEEAAAZ8ECGCfYKkWAQQQQACBcAIEcDgd1iGAAAIIIOCTAAHsEyzVIoAAAgggEE6AAA6nwzoE\nEEAAAQR8EiCAfYKlWgQQQAABBMIJEMDhdFiHAAIIIICATwIEsE+wVIsAAggggEA4AQI4nA7rEEAA\nAQQQ8EmAAPYJlmoRQAABBBAIJ0AAh9NhHQIIIIAAAj4JEMA+wVItAggggAAC4QQI4HA6rEMAAQQQ\nQMAnAQLYJ1iqRQABBBBAIJwAARxOh3UIIIAAAgj4JEAA+wRLtQgggAACCIQTiDiAN23aJL169ZIW\nLVpI27ZtZfny5c7+xo4dK40aNXIePXr0cNYxgwACCCCAQCILJEfa+Lvvvlvuu+8+6devnyxcuFD6\n9Okj27ZtM9UuXbpUpk2bJl26dDHPK1SIOO8jPVy2RwABBBBAoFwIRBzA7733ntSsWdM0pqCgQPRh\nT2vWrJH27dvL5s2bpXHjxnLWWWfZq/iJAAIIIIBAQgtEHMBpaWkGcOjQoTJ37lzJzMw0z7dv3y4H\nDhyQzp07y759++TgwYMyb948SU9PDwn++eefmx5zSQUOHz4stWvXlunTp5e0mmUIIIAAAgjElEDE\nAaytzc/Pl3POOUcaNGggb775pnTv3l2OHDkiAwcOlIkTJ0r16tVl/PjxMmHChLAB3KZNG5k0aVKJ\ngBs2bDB1l7iShQgggAACCMSYQFLAmrw6Zr38XK9ePROUxXu6ubm5Ur9+fdmxY4fpyZ7uPrOzsyUr\nK0umTJlyuptSHgEEEEAAgXInENGoqKNHj8rIkSNND1hblpycLE2bNjX3fFevXi0zZ850Gqy95EqV\nKpnesLOQGQQQQAABBBJUIKIATklJkZUrV8qMGTMM34oVK+Trr7+WTp06mV7ukCFDJCcnR06cOGHu\nDWdkZIhuw4QAAggggECiC0R8D1jv6w4fPlwmT54sNWrUkFdeeUWaN29uXMeMGSMautr7TU1NNYO0\nEh2c9iOAAAIIIKACnt0D3r9/vwng4qx6izkvL0/s0dLF17t9zj1gt1KUQwABBBCIBYGILkEXbqD2\nfkuakpKSIg7fkuplGQIIIIAAArEs4FkAxzICx44AAggggEBZCxDAZS3O/hBAAAEEELAECGBeBggg\ngAACCERBgACOAjq7RAABBBBAgADmNYAAAggggEAUBAjgKKCzSwQQQAABBAhgXgMIIIAAAghEQYAA\njgI6u0QAAQQQQIAA5jWAAAIIIIBAFAQI4Cigs0sEEEAAAQQIYF4DCCCAAAIIREGAAI4COrtEAAEE\nEECAAOY1gAACCCCAQBQECOAooLNLBBBAAAEECGBeAwgggAACCERBgACOAjq7RAABBBBAgADmNYAA\nAggggEAUBAjgKKCzSwQQQAABBAhgXgMIIIAAAghEQYAAjgI6u0QAAQQQQIAA5jWAAAIIIIBAFAQI\n4Cigs0sEEEAAAQQIYF4DCCCAAAIIREGAAI4COrtEAAEEEECAAOY1gAACCCCAQBQECOAooLNLBBBA\nAAEECGBeAwgggAACCERBgACOAjq7RAABBBBAgADmNYAAAgh4KPD888/LyZMnPayRquJVgACO1zNL\nuxBAICoC7733HgEcFfnY2ykBHHvnjCNGAAEEEIgDAQI4Dk4iTUAAAQQQiD2BiAN406ZN0qtXL2nR\nooW0bdtWli9f7igsWbJEOnbsKI0bNzZl9u7d66xjBgEEEEAAgUQWiDiA7777bunbt6+sW7dOxo0b\nJ3369DGeubm50q9fP5k6dapoSGsIjxgxIpGtaTsCCCCAAAKOQLIzV8oZHXBQs2ZNs3VBQYHoQ6cV\nK1ZIs2bNpGXLlub54MGDpXXr1vLyyy+b5/yDAAIIIIBAIgtEHMBpaWnGb+jQoTJ37lzJzMw0z3Ny\ncqRu3bqObZ06dWT//v2Sn58vlStXdpYzgwACCCCAQCIKRBzAiqahes4550iDBg3kzTfflO7du8ue\nPXukWrVqjmmVKlXM/OHDh0MG8IIFC2TChAnONoVnDh06JHYdhZczjwACCCCAQCwKeBLA2qMdNWqU\njBw5UurVqyfLli2TWrVqydq1ax2TgwcPSkpKiqSmpjrLis9069ZN9FHSlJ2dLVlZWSWtYhkCCCCA\nAAIxJxDRIKyjR4+a0NUesE7JycnStGlT2bx5s+kNb9261SzXf3S+YcOGznNmEEAAAQQQSGSBiAJY\ne7QrV66UGTNmGEMdePX1119Lp06dJD09XbZs2SKLFi0yl6gnTZokvXv3TmRr2o4AAggggIAjEPEl\naL1nO3z4cJk8ebLUqFFDXnnlFWnevLnZgQ7I6tmzp1muPWP9jlQmBBBAAAEEELCuGkeKoF++ofd8\ndYSzBnDhST8frF/Sofd/w937LbwN8wgggAACCCSCQESXoAsDFQ9fe53eFyZ8bQ1+IoAAAggg8H8C\nngUwoAgggAACCCDgXoAAdm9FSQQQQAABBDwTIIA9o6QiBBBIdIFAICD6LYDff/99olPQfhcCBLAL\nJIoggAACbgR2795t/vjMhx9+6KY4ZRJcgABO8BcAzUcAAe8ETp48aSqzf3pXMzXFowABHI9nlTYh\ngAACCJR7AQK43J8iDhABBBBAIB4FCOB4PKu0CQEEEECg3AsQwOX+FHGACCCAAALxKEAAx+NZpU0I\nIIAAAuVegAAu96eIA0QAAQQQiEcBAjgezyptQgABBBAo9wIEcLk/RRwgAggggEA8ChDA8XhWaRMC\nCCCAQLkXIIDL/SniABFAAAEE4lGAAI7Hs0qbEEAAAQTKvQABXO5PEQeIAAIIIBCPAgRwPJ5V2oQA\nAgggUO4FCOByf4o4QAQQiBWBH374wRzqzp07Y+WQOc4oChDAUcRn1wggED8CP/30k9x0002mQePG\njZMFCxbET+NoiS8CBLAvrFSKAAKJJvDBBx9Ibm6u0+znnnvOmWcGgZIECOCSVFiGAAIInKbAeeed\nJydPnjRbVahQQRo0aHCaNVA80QQI4EQ747QXAQR8Ebjqqqtk6tSppu7rrrtOpk2b5st+qDR+BAjg\n+DmXtAQBBKIs0K1bN3MEN9xwg2gvmAmBcAK8QsLpsA4BBBBAAAGfBAhgn2CpFgEEEEAAgXACBHA4\nHdYhgAACCCDgkwAB7BMs1SKAAAIIIBBOgAAOp8M6BBBAAAEEfBIggH2CpVoEEEAAAQTCCRDA4XRY\nhwACCCCAgE8CBLBPsFSLAAIIIIBAOAECOJwO6xBAAAEEEPBJIOIAXr9+vdx6663SqlUr6dq1q8yZ\nM8c51LFjx0qjRo2cR48ePZx1zCCAAAIIIJDIAsmRNn7o0KFy2223yezZs2XXrl3SunVrueaaa6RO\nnTqydOlS832oXbp0Mbvhq9ki1WZ7BBBAAIF4EYioB6x/+eP+++83PWAFqVevnlSvXl1WrVplfNas\nWSPt27eXzZs3S0FBgaSkpMSLG+1AAAEEEEAgIoGIAlh7tD179pSKFSuag1i0aJHs3btXOnToINu3\nb5cDBw5I586dpXv37tKwYUNZvHhxRAfLxggggAACCMSLQMSXoG2ITZs2yYABAyQzM1POPvts+eGH\nH2TgwIEyceJE0yseP368TJgwQdLT0+1Ngn4uWLDAlAlaYS04dOiQVKlSpaRVLEMAAQQQQCDmBJIC\n1hTpUW/YsMEE6+OPPy6DBg0qsbrc3FypX7++7NixQ2rXrl1imXALs7OzJSsrS6ZMmRKuGOsQQACB\nqAkcPXpU6tatK/Pnz5err746asfBjmNDIKJL0NrELVu2SEZGhowePbpI+K5evVpmzpzpKOTn50ul\nSpVMb9hZyAwCCCAQRwI6zqVNmzbSrl27OGoVTfFLIOIA1svO/fv3NwOx8vLyRB/Hjh0zvdwhQ4ZI\nTk6OnDhxwlya1qBmIJZfp5J6EUAAAQRiSSCie8DLly+XL774wjyefvppp93a89X7v2PGjDG9Y+39\npqamyty5c50yzCCAAAIIIJDIAhEF8JVXXinhbiEPHz5chg0bZnrFaWlpiexM2xFAAAEEECgiEPEl\n6CK1lfAkKSlJCN8SYFiEAAIIIJDQAr4HcELr0ngEEEAAAQRCCBDAIWBYjAACCCCAgJ8CBLCfutSN\nAAIIIIBACAECOAQMixFAAAEEEPBTgAD2U5e6EUAAAQQQCCFAAIeAYTECCCCAAAJ+ChDAfupSNwII\nIIAAAiEECOAQMCxGAAEEEEDATwEC2E9d6kYAAQQQQCCEAAEcAobFCCCAAAII+ClAAPupS90IIIAA\nAgiEECCAQ8CwGAEEECiNgP7lN/0OfCYETiUQ0V9DOlXlrEcAAQQSTeCtt95KtCbT3lIK0AMuJRyb\nIYAAAgggEIkAARyJHtsigAACCCBQSgECuJRwbIYAAggggEAkAgRwJHpsiwACCCCAQCkFCOBSwrEZ\nAggggAACkQgQwJHosS0CCCCAAAKlFCCASwnHZggggAACCEQiQABHose2CCCAAAIIlFKAAC4lHJsh\ngAACCCAQiQABHIke2yKAAAIIIFBKAQK4lHBshgACCCCAQCQCBHAkemyLAAIIIIBAKQUI4FLCsRkC\nCCCAAAKRCBDAkeixLQIIIIAAAqUUIIBLCcdmCCCAAAIIRCJAAEeix7YIIIAAAgiUUoAALiUcmyGA\nAAIIIBCJAAEciR7bIoAAAgggUEoBAriUcGyGAAIIIIBAJAIEcCR6bIsAAggggEApBSIO4PXr18ut\nt94qrVq1kq5du8qcOXOcQ1myZIl07NhRGjduLL169ZK9e/c665hBAAEEEEAgkQUiDuChQ4fKdddd\nJ2vWrJFXX31VhgwZIt9//73k5uZKv379ZOrUqbJp0yYTwiNGjEhka9qOAAIIIICAI5DszJVi5uTJ\nk3L//fdL9+7dzdb16tWT6tWry6pVqyQpKUmaNWsmLVu2NOsGDx4srVu3lpdffrkUe2ITBBBAAAEE\n4ksgoh5whQoVpGfPnlKxYkWjsmjRInOZuUOHDpKTkyN169Z1tOrUqSP79++X/Px8Z1nxGQ30o0eP\nlvjQ7XQ9EwIIIIAAAvEgEFEPuDCAXmYeMGCAZGZmytlnny179uyRatWqOUWqVKli5g8fPiyVK1d2\nlheeWbx4sUyaNKnwImf+4MGDkpzs2eE69TKDAAIIIIBANAQ8SbQNGzZIenq6PP7442ZAljakVq1a\nsnbtWqdNGqApKSmSmprqLCs+k5GRIfooacrOzpasrKySVrEMAQQQQACBmBOI6BK0tnbLli0mNEeP\nHi2DBg1yABo0aCBbt251nut8w4YNnefMIIAAAgggkMgCEQewXnbu37+/6fnm5eWJPo4dO2Z6xBrO\nel9Y79/qpeXevXsnsjVtRwABBBBAwBGIKICXL18uX3zxhTz99NOSlpbmPGbPnm3u8+r9YB2k1aRJ\nE9m+fbtoL5kJAQQQQAABBEQiugd85ZVXSiAQCOnYt29f8wUcev833L3fkBWwAgEEEEAAgTgViKgH\n7MZERy4Tvm6kKIMAAgggkEgCvgdwImHSVgQQQAABBNwKEMBupSiHAAIIIICAhwIEsIeYVIUAAggg\ngIBbAQLYrRTlEEAAAQQQ8FCAAPYQk6oQQAABBBBwK0AAu5WiHAIIIIAAAh4KEMAeYlIVAggggAAC\nbgUIYLdSlEMAAQQQQMBDAQLYQ0yqQgABBBBAwK0AAexWinIIIIAAAgh4KEAAe4hJVQgggAACCLgV\nIIDdSlEOAQQQQAABDwUIYA8xqQoBBBBAAAG3AgSwWynKIYAAAggg4KEAAewhJlUhgAACCCDgVoAA\nditFOQQQQAABBDwUIIA9xKQqBBBAAAEE3AoQwG6lKIcAAggggICHAgSwh5hUhQACCCCAgFsBAtit\nFOUQQAABBBDwUIAA9hCTqhBAAAEEEHArQAC7laIcAggggAACHgoQwB5iUhUCCCCAAAJuBQhgt1KU\nQwABBBBAwEMBAthDTKpCAAEEEEDArQAB7FaKcggggAACCHgoQAB7iElVCCCAAAIIuBUggN1KUQ4B\nBBBAAAEPBQhgDzGpCgEEEEAAAbcCBLBbKcohgAACCCDgoQAB7CEmVSGAAAIIIOBWgAB2K0U5BBBA\nAAEEPBTwNICPHz/u4aFRFQIIIIAAAvEr4FkAz549Wzp06FBEauzYsdKoUSPn0aNHjyLreYIAAggg\ngECiCiRH2vC9e/fKY489Jm+99ZY0bNiwSHVLly6VadOmSZcuXczyChU8y/si++EJAggggAACsSYQ\ncSIuWrRIqlatKrNmzQpq+5o1a6R9+/ayefNmKSgokJSUlKAyLEAAAQQQQCARBSLuAffp00f0sWTJ\nkiJ+27dvlwMHDkjnzp1l3759cvDgQZk3b56kp6cXKVf4iZbftWtX4UXO/JYtW+Tw4cPOc2YQQAAB\nBBCIZYGIAzhU448cOSIDBw6UiRMnSvXq1WX8+PEyYcKEsAG8fv36EnvSuo+8vDzZv39/qN2xHAEE\nEEAAgZgSSApYkxdHrD3gESNGyMqVK0usLjc3V+rXry87duyQ2rVrl1gm3MLs7GzJysqSKVOmhCvG\nOgQQQAABBGJCIOJ7wKFauXr1apk5c6azOj8/XypVqmR6w85CZhBAAAEEEEhQAd8CWHu5Q4YMkZyc\nHDlx4oRkZmZKRkYGA7ES9IVGsxFAAAEEigr4dg9YLzePGTPGhK72flNTU2Xu3LlF984zBBBAAAEE\nElTAs3vAofz0FrMOoEpLSwtVxNVy7gG7YqIQAggggECMCPh2Cdpuf1JSUsTha9fFTwQQQAABBOJF\nwPcAjhco2oEAAggggICXAgSwl5rUhQACCCCAgEsBAtglFMUQQAABBBDwUoAA9lKTuhBAAAEEEHAp\nQAC7hKIYAggggAACXgoQwF5qUhcCCCCAAAIuBQhgl1AUQwABBBBAwEsBAthLTepCAAEEEEDApQAB\n7BKKYggggAACCHgpQAB7qUldCCCAAAIIuBQggF1CUQwBBBBAAAEvBQhgLzWpCwEEEEAAAZcCBLBL\nKIohgAACCCDgpQAB7KUmdSGAAAIIIOBSgAB2CUUxBBBAAAEEvBQggL3UpC4EEEAAAQRcChDALqEo\nhgACCCCAgJcCBLCXmtSFAAIIIICASwEC2CUUxRBAAAEEEPBSgAD2UpO6EEAAAQQQcClAALuEohgC\nCCCAAAJeChDAXmpSFwIIIIAAAi4FCGCXUBRDAAEEEEDASwEC2EtN6kIAAQQQQMClAAHsEopiCCCA\nAAIIeClAAHupSV1FBGbNmiUXXXSRpKamyr59+4qs4wkCCCCQ6AIEcKK/Anxq/8qVK+WOO+6QTZs2\nmfC99957fdoT1SKAAAKxKUAAx+Z5K/dHvWfPHqldu7ZznEuXLnXmmUEAAQQQEEkGAQE/BLp27Srn\nn3++HDlyRM444wx55513/NgNdSKAAAIxK0AAx+ypK98HrqH75ZdfyldffSV169aVRo0ale8D5ugQ\nQACBMhYggMsYPNF2165du0RrMu1FAAEEXAlwD9gVE4UQQAABBBDwVsDTAD5+/Li3R0dtCCCAAAII\nxKmAZwE8e/Zs6dChQxGmJUuWSMeOHaVx48bSq1cv2bt3b5H1PEEAAQQQQCBRBSIOYA3VBx98UB56\n6CEJBAKOY25urvTr10+mTp1qPguqITxixAhnPTMIIIAAAggkskDEAbxo0SKpWrWq6LceFZ5WrFgh\nzZo1k5YtW0rFihVl8ODB8u677xYuwjwCCCCAAAIJKxDxKOg+ffqIPvRyc+EpJyfHfPzEXlanTh3Z\nv3+/5OfnS+XKle3FRX7u3LlT1q5dW2SZ/WTr1q2Sl5dnP+UnAggggAACMS0QcQCHar1+E1K1atWc\n1VWqVDHzhw8fDhnA+n3B69atc7YpPLN79245dOhQ4UXMI4AAAgggELMCvgVwrVq1ivRmDx48KCkp\nKeaL+UNpXXLJJaKPkqbs7GzJysoqaRXLEEAAAQQQiDmBiO8Bh2pxgwYNRC8b25PON2zY0H7KTwQQ\nQAABBBJawLcATk9Ply1btogO0tL7vpMmTZLevXsnNDaNRwABBBBAwBbw7RK0DrTKzMyUnj17So0a\nNaRp06by/PPP2/vlJwIIIIAAAgktkGR9dvf/f3jXB4qCggLR+7/6R9kjmex7wFOmTImkGrZFAAEE\nEECgXAj4dgnabl1ycnLE4WvXxU8EEEAAAQTiRcD3AI4XKNqBAAIIIICAlwIEsJea1IUAAggggIBL\nAQLYJRTFEEAAAQQQ8FKAAPZSk7oQQAABBBBwKUAAu4SiGAIIIIAAAl4KEMBealIXAggggAACLgUI\nYJdQFEMAAQQQQMBLAQLYS03qQgABBBBAwKUAAewSimIIIIAAAgh4KUAAe6lJXQgggAACCLgUIIBd\nQlEMAQQQQAABLwUIYC81qQsBBBBAAAGXAgSwSyiKIYAAAggg4KUAAeylJnUhgAACCCDgUoAAdglF\nMQQQQAABBLwUIIC91KQuBBBAAAEEXAoQwC6hKIYAAggggICXAgSwl5rUhQACCCCAgEsBAtglFMUQ\nQAABBBDwUoAA9lKTuhBAAAEEEHApQAC7hKIYAggggAACXgoQwF5qUhcCCCCAAAIuBQhgl1AUQwAB\nBBBAwEsBAthLTepCAAEEEEDApQAB7BKKYggggAACCHgpQAB7qUldCCCAAAIIuBQggF1CUQwBBBBA\nAAEvBQhgLzWpCwEEEEAAAZcCBLBLKIohgAACCCDgpQAB7KUmdSGAAAIIIOBSgAB2CUUxBBBAAAEE\nvBQggL3UpC4EEEAAAQRcChDALqEohgACCCCAgJcCvgbw2LFjpVGjRs6jR48eXh47dSGAAAIIIBCz\nAsl+HvnSpUtl2rRp0qVLF7ObChV8zXs/m0LdCCCAAAIIeCrgayKuWbNG2rdvL5s3b5aCggJJSUnx\n9OCpDAEEEEAAgVgV8K0HvH37djlw4IB07txZ9u3bJwcPHpR58+ZJenp6SKuNGzfK4sWLS1y/a9cu\n0QcTAggggAAC8SDgWw/4yJEjMnDgQFm2bJls27ZNRowYIRMmTAhrVrlyZUlLSyvxUaNGDalYsWLY\n7VmJAAIIIIBArAgkBaypLA42NzdX6tevLzt27JDatWuf9i6zs7MlKytLpkyZctrbsgECCCCAAALl\nTcC3HvDq1atl5syZTnvz8/OlUqVKUr16dWcZMwgggAACCCSqgG8BrL3cIUOGSE5Ojpw4cUIyMzMl\nIyODgViJ+kqj3QgggAACRQR8G4Sll5vHjBljQld7v6mpqTJ37twiO+cJAggggAACiSrgWwAr6PDh\nw2XYsGGSl5dnBlYlKjLtRgABBBBAoLiAb5eg7R0lJSURvjYGPxFAAAEEEPifgO8BjDQCCCCAAAII\nBAsQwMEmLEEAAQQQQMB3AQLYd2J2gAACCCCAQLAAARxswhIEEEAAAQR8FyCAfSdmBwgggAACCAQL\nEMDBJixBAAEEEEDAdwEC2HdidoAAAggggECwAAEcbMISBBBAAAEEfBcggH0nZgcIIIAAAggECxDA\nwSYsQQABBBBAwHcBAth3YnaAAAIIIIBAsAABHGzCEgQQQAABBHwXIIB9J2YHCCCAAAIIBAsQwMEm\nLEEAAQQQQMB3AQLYd2J2gAACCCCAQLAAARxswhIEEEAAAQR8FyCAfSdmBwgggAACCAQLEMDBJixB\nAAEEEEDAdwEC2HdidoAAAggggECwAAEcbMISBBBAAAEEfBcggH0nZgcIIIAAAggECxDAwSYsQQAB\nBBBAwHcBAth3YnaAAAIIIIBAsAABHGzCEgQQQAABBHwXIIB9J2YHCCCAAAIIBAsQwMEmLEEAAQQQ\nQMB3AQLYd2J2gAACCCCAQLAAARxswhIEEEAAAQR8FyCAfSdmBwgggAACCAQLEMDBJixBAAEEEEDA\ndwEC2HdidoAAAggggECwAAEcbMISBBBAAAEEfBcggH0nZgcIIIAAAggEC/gawEuWLJGOHTtK48aN\npVevXrJ3797gI2AJAggggAACCSjgWwDn5uZKv379ZOrUqbJp0yYTwiNGjEhAYpqMAAIIIIBAsIBv\nAbxixQpp1qyZtGzZUipWrCiDBw+Wd999N/gIWIIAAggggEACCiT71eacnBypW7euU32dOnVk//79\nkp+fL5UrV3aWF55ZuXKlzJkzp/AiZ/7HH38UDfUxY8Y4y7p06SKdO3c2z3/66Sf505/+5KzTGdbj\nw+uD/x/6XsD7A++P4fJBXyPRmHwL4D179ki1atWcNlWpUsXMHz58OGQAn3feedK3b19nm8IzR48e\nNWGr95PtScvbU6VKlUzg2s/1J+vPczjw4fWhv5AWnvj/wf8P+/WQ6O8PtkNZ/0wKWJMfO50+fbos\nXrxYZs+ebao/cOCAaC/4yJEjfuyOOhFAAAEEEIgpAd/uATdo0EC2bt3qYOh8w4YNnefMIIAAAggg\nkMgCvgVwenq6bNmyRRYtWmTu+06aNEl69+6dyNa0HQEEEEAAAUfAt0vQuoe3335b7rrrLqlRo4Y0\nbdpUPvjgAznzzDOdnTODAAIIIIBAogr4GsCKWlBQIAcPHpTU1NRENabdCCCAAAIIBAn4HsBBe2QB\nAggggAACCIhv94CxRQABBBBAAIHQAgRwaBvWIIAAAggg4JsAAewbLRUjgAACCCAQWoAADm3DGgQQ\nQAABBHwTIIB9o6ViBBBAAAEEQgsQwKFtWIMAAggggIBvAgSwb7RUjAACCCCAQGgBAji0DWsQQAAB\nBBDwTYAA9o2WihFAAAEEEAgtQACHtmENAggggAACvgkQwL7RUjECCCCAAAKhBQjg0DasQQABBBBA\nwDcBAtg3WipGAAEEEEAgtAABHNqGNQgggAACCPgmQAD7RkvFCCCAAAIIhBYggEPbsAYBBBBAAAHf\nBAhg32ipGAEEEEAAgdACBHBoG9YggAACCCDgmwAB7BstFSOAAAIIIBBagAAObcMaBBBAAAEEfBNI\n9q1mKk5ogby8PJk2bZqsWrVKtm7dKk2bNpUrrrhC+vXrJ/Xq1UtoGxofvwLHjx+Xw4cPy8mTJ+Wj\njz6SjIwMqVOnTvw2mJZFJJAUsKaIamBjBIoJTJ48WTZv3iy/+MUvpGXLllK7dm3JycmR9evXy9y5\nc6VVq1YyatSoYlvxFIHYF9DX/MiRI+Wll16SatWqyX/+8x/59NNPY79htMAXAQLYF9bErvSbb76R\nZs2ahURYt26dXHLJJVKhAndAQiKxIuYEDh06JLfffru8/vrr0qJFC9m4caP0799fsrKy5Kyzzoq5\n9nDA/gvwDui/ccLtwQ7f999/v0jbp0+fLgUFBebNifAtQsOTOBCoUqWK7Ny5U5566ilz9Uev+Oze\nvZvwjYNz61cT6AH7JZvA9epl5vnz58tnn30mnTt3NhJ6T2zZsmXm0vQZZ5yRwDo0PZ4FvvrqK1m4\ncKE8+OCDsmTJErngggvML5zx3GbaVnoBArj0dmwZQuDAgQOyYcMGeeGFF2TQoEGmlIbuueeeK7Vq\n1QqxFYsRiH0BvQStV3kKT2+88Ubhp8wj4AgwCtqhYMYrAb3f1bZtW0lKSpLhw4fLjh07pHHjxvLs\ns88SwF4hU0+5FNDXu45r1Ss+eg/4448/LpfHyUGVDwF6wOXjPMTlUbRp00ZmzpxpBlytWbNG7rrr\nLlm5cqUJ5rhsMI1CoJjAzTffLLNmzZLq1asXW8NTBEToAfMq8EUgPz/ffPzo0ksvNfVfdtll5vOQ\n+hlJ/XgGEwLxKPDMM8/IiRMnTNP0s/D6cbwzzzwzHptKmzwQIIA9QKSKYIHKlSubLyTo0aOHXH31\n1eYLObZt22YuQ+sb0pAhQ4I3YgkCMS5Qs2ZNc/lZm6FfOPPQQw9xxSfGz6mfh88laD91E7xu/Tyk\n3gsrPqWkpEjfvn2LL+Y5AjEvwDdhxfwpLNMGEMBlys3OEEAgngX4Jqx4Prvet41L0N6bUuP/BLKz\ns80l56NHj0q7du2kefPmkp6ejg8CcSmg34Slg606duwo9913n/NNWPqxPL4JKy5PecSN4puwIiak\nglACjz/+uDz66KOib0C9e/eWJ598MlRRliMQ8wJ8E1bMn8IybwABXObkibFDvRemXzfZpEkT0+C6\ndeuKDlA5cuRIYgDQyoQT0Nf7sGHDRL90Zty4cWYE9HPPPZdwDjTYvQD3gN1bUfI0BR544AHz0aNP\nPvnE/Fm27du3y4wZM06zFoojEBsCx44dM3/9S78FjgkBNwIEsBslypRKYMuWLeYvw+zZs8d8JOnh\nhx+WCy+8sFR1sRECsSBwzTXXSMOGDc1fA7O/8/yRRx6JhUPnGKMgwCCsKKAnyi7vueceGT9+vBmA\npX+YQT/7y1fzJcrZT8x26re9lfTRu8TUoNWnEiCATyXE+lIJ6DdhVapUyYSvVqB/FSkzM1N0RLR+\nDpgJgXgU0NHOb7/9tugYCA3i7777Tu644454bCpt8kCAQVgeIFJFsIB+E1ZycrKMHj1a9O8C//73\nv5eqVasSvsFULIkTAQ1cHfWvXzKj83369OFPEcbJufWrGQSwX7LUK3PmzBEd/fzpp5/K5ZdfLllZ\nWaggELcCOsJfv/u8Z8+eZszDLbfcIjowS7//nAmBkgS4BF2SCss8EdDvftY/TM6EQCII6B8Z2bdv\nn/mFU6/2vPLKK+ajSHo1iAmBkgQYBV2SCssiFuAjGRETUkEMCug93127dpm/ez1p0iTRP0aSkZER\ngy3hkMtCgAAuC+UE3QcfyUjQE5/AzdbxDjfddJMjMH36dLnzzjvNeAhnITMI/E+AS9C8FHwT4CMZ\nvtFScTkTmDt3rsyfP1/043bz5s0zR6cDsZYtWyb6/4AJgZIECOCSVFjmiYAOvHr22WfNR4/sP8bg\nScVUgkA5E9C/gtSoUSPz9auDBg0yR6dfxPHMM8+Yr6YsZ4fL4ZQTAS5Bl5MTEY+HcfPNN8vEiRNl\n+PDh8sILL8iAAQPk73//ezw2lTYhgAACpy3Ax5BOm4wN3AjwxxjcKFEm3gXatGkT702kfREIEMAR\n4LFpaIGKFSuaP8TwxBNPyI8//ij6pwn1Yxr6J9uYEIhXAR2EVXjSL+MoKCgovIh5BBwBLkE7FMx4\nLaAfRVq4cKG57NypUye5/vrrCWCvkamvXAgUHoSlX7uqkz0Ia/PmzdwHLhdnqfwdBAFc/s5J3BwR\nH8mIm1NJQ04hcODAAdE/Q6hjHQoPwjr33HPNZ4JPsTmrE1SAAE7QE+9ns+kN+KlL3QggEC8CBHC8\nnMly1A56A+XoZHAoZSrw0UcfyWuvvSb618Ds6Z133rFn+YlAEQECuAgHT7wU4M3IS03qKu8COtiq\nRYsW8uKLL0paWppzuM2bN3fmmUGgsABfxFFYg3nPBPTNaMSIEUFvRp7tgIoQKGcCgUDAfBmHDjhk\nQsCNAAHsRokypy3Am9Fpk7FBjAvoR+/02690tH+HDh2ckc+jRo2K8ZZx+H4JEMB+ySZ4vbwZJfgL\nIEGb379/f/PxowRtPs0+TQEC+DTBKO5egDcj91aUjA+BVq1a8f3n8XEqy6QVDMIqE2Z2ggACiSDA\n958nwln2ro30gL2zpKb/Cdx4442yc+fOEj1WrVpV4nIWIhDrAuG+/5yvYI31s+vP8RPA/rgmdK1/\n+ctf5MSJEwltQOMTT4DvP0+8cx5pi/ljDJEKsn2QwHPPPSdJSUlSr169oMemTZtk2LBhBHSQGgvi\nQWDy5Mmifwe7bdu2oveDp06dGg/Nog0+CXAP2CfYRK42NzdXxo8fL998841cfPHFUrt2bcnJyZGN\nGzdKkyZNZNy4cVK3bt1EJqLtcSqwY8cO87q/9tprzfdC33DDDdKgQYM4bS3NilSAAI5UkO1DCuTl\n5cm6detk69at0rRpU9MjqFq1asjyrEAg1gUyMjLML5/t2rWTzz77TJ566in5+OOPY71ZHL9PAgSw\nT7BUiwACiSWg3//cq1cv0a9gtae+ffvKq6++KikpKfYifiLgCDAIy6FgBgEEECi9QOXKlSU5OVlG\njx5t7gHriH+94kP4lt403rekBxzvZ5j2IYBAmQkcOXJEXnrpJfn222+lS5cu0q1bNwK4zPRjb0cE\ncOydM44YAQQQQCAOBPgYUhycRJqAAAIIIBB7AgRw7J0zjhgBBBBAIA4ECOA4OIk0AQEEEEAg9gQI\n4Ng7ZxwxAggggEAcCBDAcXASaQICCCCAQOwJEMCxd844YgQQQACBOBAggOPgJNIEBBBAAIHYEyCA\nY++cccQIIIAAAnEgQADHwUmkCQgggAACsSdAAMfeOeOIEUAAAQTiQIAAjoOTSBMQQAABBGJPgACO\nvXPGESOAAAIIxIHA/wNOD5Loc1x1MwAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 115
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Interpreting coeffi\u000ecients: Making sense of the slope\n",
      "\n",
      "One thing to keep in mind is what the estimated slope 26.9 is telling us. It is\n",
      "saying that for every increase by \"1\" unit of tarsus (of whatever unit tarsus\n",
      "is measured in), the number of `SCT` is predicted to increase by 26:9. However,\n",
      "let us look at the range of tarsus values."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(quantile(dll.data$tarsus))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "   0%   25%   50%   75%  100% \n",
        "0.106 0.175 0.188 0.200 0.258 \n"
       ]
      }
     ],
     "prompt_number": 116
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The range of tarsus lengths is between 0.10 $-$ 0:258, so a change of unit length\n",
      "(i.e. from 0.10 to 1.1) goes far outside the biologically plausible range for this\n",
      "variable.\n",
      "\n",
      "What can we do to interpret the slope? One thing you can do is just interpret\n",
      "carefully. Instead of thinking about what happens if we increase tarsus length by\n",
      "1, we can instead think about what we would predict if tarsus length increased\n",
      "by 0.1 (we would predict an increase of 26.9/10 = 2.69 `SCT` for a 0.1 increase in\n",
      "tarsus). This is much more reasonable, and easier to explain.\n",
      "\n",
      "In this instance you can think about how the range of values for tarsus length\n",
      "is\u0000"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(range(dll.data$tarsus))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "[1] 0.106 0.258\n"
       ]
      }
     ],
     "prompt_number": 117
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "or"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(max(dll.data$tarsus) - min(dll.data$tarsus))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "[1] 0.152\n"
       ]
      }
     ],
     "prompt_number": 118
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Which is \u0018~ 0.15mm. So we can just calculate 0.15 \u0003* 26.9, the slope times\n",
      "the range of values. So over the whole range of values for tarsus we increase\n",
      "SCT by 4.035. Is this a lot? Let's compare it to the standard deviation for the\n",
      "observed sample."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(sd(dll.data$SCT))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "[1] 1.63\n"
       ]
      }
     ],
     "prompt_number": 119
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It is \u0018~ 2\u0003$\\times$ greater than the sd for SCT, suggesting that tarsus length is probably\n",
      "a biologically (as well as statistically) signifi\f",
      "cant covariate for accounting\n",
      "for variation for SCT. In combination with $R^2$, I fi\f",
      "nd I am usually able to think\n",
      "about the biological importance of my variables in this manner. We will go\n",
      "through a more formal analysis for eff\u000b",
      "ect sizes in the coming weeks.\n",
      "It is also important to remember that there is uncertainty in your point\n",
      "estimate, so it is worth doing this for the confi\f",
      "dence intervals."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(confint(regression.2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "            2.5 % 97.5 %\n",
        "(Intercept)  11.1   11.2\n",
        "cent.tarsus  23.0   30.8\n"
       ]
      }
     ],
     "prompt_number": 120
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So the lower bounds for the estimate is 0.15 $*$\u0003 23.01 ~\u0018 3.5 SCT. The upper\n",
      "bound is 0.15\u0003$*$30.8 \u0018~ 4.62 SCT. Neither of these really changes our interpretation\n",
      "of the biological importance of tarsus length as a covariate.\n",
      "\n",
      "# Interpreting the slope II: You could also recode tarsus length to micrometres instead of mm\n",
      "\n",
      "We could also just rescale our tarsus measures from milli-metres to micro-metres."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "dll.data$cent.tarsus.microM <- 1000*dll.data$cent.tarsus\n",
      "\n",
      "regression.3 <- lm(SCT ~ cent.tarsus.microM, data=dll.data )\n",
      "\n",
      "print(coef(regression.3))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "       (Intercept) cent.tarsus.microM \n",
        "           11.1324             0.0269 \n"
       ]
      }
     ],
     "prompt_number": 121
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This will not change anything other than the estimate for the slope and its\n",
      "SE (both 1000 times smaller). This may make it easier to interpret, as a unit\n",
      "increase in tarsus length (1 microM), increases expected number of SCT by\n",
      "\u0018~ 0.0269.\n",
      "\n",
      "# Interpreting the slope III: Data normalization\n",
      "\n",
      "You could also normalize the data by dividing all values of tarsus by `sd(tarsus)`.\n",
      "If you do this on the centered data, it is called unit standardized data.\n",
      "You can also accomplish this using `scale(x, center=T, scale=T)`. Note\n",
      "that `scale=T` now.\n",
      "\n",
      "If you normalize/standardize like this then you are no longer thinking in\n",
      "units of the measured variable, but in changes in units of standard deviation.\n",
      "This can be very useful for covariates that are diffi\u000ecult to compare (say nutrient\n",
      "concentration and water temperature). However it does add some complication\n",
      "to interpretation. I should also point out that several people (David Houle being\n",
      "a strong member of this community) suggest that more often scaling by the\n",
      "mean, not the standard deviation makes sense. I am happy to share references\n",
      "if you are interested. This form of re-scaling of data (either mean or sd) is\n",
      "very commonly done when estimating natural selection, so that estimates can\n",
      "be compared across studies.\n",
      "\n",
      "Let's take a look how it influences our estimates."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "dll.data$tarsus.std <- as.numeric(scale(dll.data$tarsus))\n",
      "regression.4 <- lm(SCT ~ tarsus.std, data=dll.data )\n",
      "print(summary(regression.4)$coef[,1:2])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "            Estimate Std. Error\n",
        "(Intercept)   11.132     0.0355\n",
        "tarsus.std     0.481     0.0355\n"
       ]
      }
     ],
     "prompt_number": 122
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The estimate for the slope and its SE have changed. What do they mean?\n",
      "They are now in units of standard deviations of the `tarsus`. I \f",
      "find it helps to\n",
      "think about the range of new values."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(range(dll.data$tarsus.std))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "[1] -4.55  3.94\n"
       ]
      }
     ],
     "prompt_number": 123
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is now in terms of sd of the original variable (tarsus length) so the min\n",
      "value is -4.5 sd from the mean of tarsus length, and max \u0018~ 3.9 sd from the\n",
      "mean. But how much is a sd unit for tarsus?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(sd(dll.data$tarsus))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "[1] 0.0179\n"
       ]
      }
     ],
     "prompt_number": 124
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So a sd \"unit\" is \u0018~ 0.018 mm of tarsus length. The slope is now interpreted\n",
      "as saying for every increase of 1 sd in tarsus length, SCT number increases by ~ 0.48"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "plot(jitter(SCT) ~ tarsus.std , data=dll.data )\n",
      "abline(regression.4)\n",
      "\n",
      "new_tarsus.4 <- data.frame(tarsus.std = seq(-4.5, 4, by=0.01) )   # Makes a new data frame\n",
      "\n",
      "# \"predict\" values for our new values of tarsus\n",
      "predicted.model.4  <-predict(regression.4, new_tarsus.4 , interval=\"confidence\")\n",
      "\n",
      "#Then we add these lines back on\n",
      "lines(x = new_tarsus.4[,1], y = predicted.model.4[,1], lwd=3) # this would be the same as abline(model.1)\n",
      "lines(x = new_tarsus.4[,1], y = predicted.model.4[,3], lwd=2, lty=2)\n",
      "lines(x = new_tarsus.4[,1], y = predicted.model.4[,2], lwd=2, lty=2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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XHsH3xje+MQd/GxAt8+24CFyaZSUphHPPe94z6zYj/H/6p38aP+WGP9Pw73zn\nO4+OV1WI1tfKNLbgqxNOOKE76KCDuhvf+MajfefxhvXklre8ZZqIn/GMZ+QE6Je//OWmu3LhC184\nA834vZu87GUvq+CzBsaUr2WCnhKo2m33IcDXepKTnKR77nOfmxcnIAgBP/GJT0yteKNXTNvg/+Tf\nnDYIB+l/9atf7ZAYs+15znOeLHlIa9x333032pVtP07wGBHFzT8qgKwN+EjqIhe5SPoJWRtoTPym\nNMXznve8G+rrJz/5yY6mDSMme+ffLwplCGZDON/97neTMJm3r3Od60x1DkFwTKs0evLSl760U9ie\nnPrUp87tzdRsm/t2vetdr3vqU5/aXfayl03i/8EPfpD1kgVkzUvcA5NKE0yv5H73u1/3mMc8pnvs\nYx+7qW4pa+h6PaeeWeI+8gWXTI9AEfD0WNWeuwwBmpJBeyg0Jibpjcq9733v7oc//GEO9oKMmh9w\nNf+mwVp9Yb7EN73pTR3f6a1vfescyNvAv9H+bOdxyt097nGPSzM+0yxztJrJ17zmNUfdOPzwwzMI\n62pXu1qSM+3+qKOOGn2/njcijk2emLGR4GlOc5ruWte6VpICDBEo0hcUpYbzNATMFP6QhzwknwE+\nTvfEJOHVr351d+Yznznvi3ss2ldt6Cc/+ckZeIWM3GPX6v6f4QxnyOtb6XpYBvSdRcAEhbXjla98\nZffud787Tdm2vfe9751q8sXs+4//+I/d17/+9Twv7dSkQXTyda973RH56ouJyfB+rNS/abbDFsaw\ndu0sOItgcp+m7wuzT/gE9oREhGkfhcT3xLXWRU6HwPvf//7+Fre4RR+D4OiAGAj7iNIdfV7Pmze/\n+c19DH5L2rvXve7VP+tZz1q1mSDd/klPetKSfcKU2d/0pjddsm2RP4SW1Yf5vA8N0OLl/qpXvWof\n5v3+kY98ZGISRDbT7ge59KFd9zGJynZ/8Ytf9KFR57liEtAHwfVRr7gP83YfE5w+yHfF89vnbne7\nWx+Tgj5Itg/td8m+L3zhC/vQpkfbwtTaX/rSl85rdH+DcEffTfMmiLUP83TvHpMg3T609j7M5n34\nkXNbTN7yOWyfc+OEf55dWIdm27/rXe/qb3CDG/ShnfehxfdhHs77oY9NgjD7mCi1j/UaCMAuotXn\ngkX5gBdmKlQd2W4EaGFnOtOZMpozBq8uiLITMNQiO9fbH/42xzKtNuEv/NSnPtU+Tv1KM9opwVdM\nzTRZ5k2m2GOOOab71a9+1d3//vfvHv7wh2cUNM1ulvK5z30u22bmJ9bc8j/TgkUkX/7yl+/udKc7\nZbAUbZV2NklompbPXO5yl0tf9dWvfvXURoemVG6JZkbXBp+q5UXHHntsatc04fWI/nBz0JIJjdT9\n/ou/+IuRBskCIiiP+Xg14Xd1zTRx2j9/umfu4x//eHezm90s1yRrg1ldoBjtXf9LFgOBIuDFuA/V\nizkhwHRoMPy3f/u39GFZx3na0552Q71x3Be+8IUlxyJlfsPV5C//8i+717zmNUkc9jMY89P91V/9\n1WqHLcx3SIAJlPmeKZJp8lGPelQuwdFJEwm+9lkKrJm5m7REEKHG5Prbc53rXLkWl0lf4NQRRxzR\ndl3yyvTL5Hyb29wmJ07IkN/asigSmnV38MEHd8zrsxLR0khzKM5p/fRQJCjhV11NxBqY+DTRzu1u\nd7uMPnd8aO/dt771rS40/AwKs3bX+5LFQKAIeDHuQ/VijgiIYrWUxHrUplFtpDsG8be85S1JpgJg\naGJh4s6EGqu155z8fwZO/sa//uu/Tj8mbWUnCJJqWqC+S7RhG62RdozUaGOzlKtc5SqpLVp7imBo\ni4joCU94Qq7NFdQmOIhW2NYhTzq/fgraauIemDCJnDYxc//4alvSibbfZl7DZLyENP/7v/87E5e0\nYCZtS/JBqxUYuJqc7nSn6z74wQ+OdhH0xc9rO+EflvxEZi4+ZfemZHEQmO20dHGuq3pSCGw7ArQy\nGpdEFAY8pCQQZhpSt5yFNvONb3wjNTBa5E4RhPLQhz60o8lLtCHwSvAPEz8zsImI6OdZC3cBTVu2\nMBqloC9BYJYCHX/88RnRjoyGLoHxPhx44IGpEZqEuU/2Za52L72aUAhqmqVY8sZ8zcJx5StfOaO4\nI34gMTz00EM7CT5o7Z4HE4vVBKEK4DPhs/4aAYswh4sgNebuiC/IfVZrp76bDwL78DzP59Tbe1ba\nDf+Ih7KkECgEZosA/7mBngYpz3MEKWXEsEkIs+h2Cc2VRsy3bw1uWxa12vmZ//Wbv5rmbE2y61mN\nuFdrb9rv/vVf/zVzKCN40e5cD1wWTNE03+FSp9XaZNIWe+C6TSJcyzvf+c60QNDcd2MmrtXwWO93\nYhVYOjyz2y1FwNuNeJ2vENilCFgKRIO3XGfWWuNWQ2b5kcAumi9NvmTvIDBPAi4T9N55zupKC4Et\nRYAJ2N9OFC4AfyWFwHYicKLtPFmdqxAoBAqBQqAQKAT+gEARcD0JhUAhUAgUAoXAHBAoAp4D6HXK\nQqAQKAQKgUKgCLiegUKgECgECoFCYA4IVBDWHECvUxYC80RA8gnJGUT8TrvUZSv7K1OWClL6pZrQ\nuc997q08Xa7Bfetb35rLfaxXVpKypBCYBwIrErAfhRyin/nMZ7LSiAXe1pNZXjDrtHKTLtzCctlc\ntuNck85f2wqB3YiAbEgqNFmfq4zfi170ok4ijXnJz372s1y3anyRG1naRxWItmopkDwAf//3f58Z\ny6TNlDhEHmnJPGYprsu6aOt6nUeCENdYUggMEVhmgpaXw0MqC4zkFVExJhd0S41msbLE5VKkzTJR\nvMTjn//857NfcumakcrlKhuQH8Za+VCHF1TvC4FCYDICfmPSQj7nOc/pFFKXoB8xtGIRiijICIWQ\nZbCSxnCrRTlINZMf//jHJzFaSyyLk0xQXvVXtiglBVcT45bJhJSXrkEGrPEcQ/JFy9ilfB5lQrIL\nY4tCHOouz0rgZvx0fgUipMi87W1v26ldXFIIDBFYQsAqmEi9poj1hz/84cyl6oeKcGWL8UO1WN1+\nqobI8zoL8YNQqYP4IarDqW25UU844YTcNovzVBu7EwHWEokUmDBLVkZAoQlk00y8Uh7SBpljFStA\nyOrImmyf97znzZSaK7f2h29kXJK/Gump9Sub03qEpij9YhPnlcIyyvVlfdu3ve1tnT/jjpzMTWS1\nk0O5ifSLCg/YRyEFYxgSHsqPfvSjLKrQ8iT7joXN+l/P0KxE7WDYKvCh0IPMVIifpr0dIsOWnOT/\n/u//vh2nm/k5FPaQptNE0OTLfdu1ErO0kcRssI8ZaB8zuNG2ld7EYNfHj2elr9e1PUqZ9R/96Efz\nmNB6ezUrm6gzqk7nZqXqAW8WwcU8/gUveEEfCff70DD6GPT6KMO2mB1dpVdBJH0QYB/FF/oYpEc1\nblc5ZENfBRn0UWZvybHhe+0jBWN/sYtdrI8UiEu+i+ISfWhtS7YNP0S+6z6It1ebNwivP+yww/q7\n3vWufQyeWVc3yvj1UZ6wD2vZ8LAl70PD7WMC3gdZ9kHgvVq5tkWO5iX76Zt2jRORYrK/xjWu0Yfm\n3EcFpj6qIvVhSl5ShzkmAn0oE31k5hq1E8UhskZxFHDoQ6PuY4Kf36sBHAQ82m+zb6597Wvndbdx\nNCY4Wf8XVlstMRHpo1BFHyUH+zB59w94wAO2+pQzbV897rBi9BGjkO2qsQ23UNBmep5hY2GhWIx6\nwGaDgiCmmQ3uu+++ayYKX8+shbZrRquOZxTZHh0qr6xaoyWFwDgCZvn8hV5pPTSlKAqf6RDH913U\nzyw9N7/5zdM8yeoUA2a6eQQlzVqCtLIebLMUMMnSNFQM4vJRvm4o6uA2y9RwuwCuz372s92DH/zg\nLLxwgQtcINNPPvKRj0wtlBuJVatprooErCRRQD41XsFgzML6IvZkvPyfvsl1fJ3rXCeLFPzP//zP\nqKSffMdwjEn2yGwuj7N80K6xCcudQg36KXey42jctFOYeI643Ji/lexjzqa9/uAHP2hNTPVqHHN+\nOZoJl5pzT5sTO8ghcWWeZwlYy/zeOqW04jOe8Yw0rQcJ5zldk0IPO0ViQp33ppVrZFnxXMy6nvSi\n4LHEBD2vTvEtS6IuIIL5yw+bxIw4/SfKvE0jkpiH9jzxz3frNY9Nc87aZ34IMJ2G1pXJ8/XCRM3n\nnfRjDY0xTW2KBpiEIgzuHUXVmV1nKUx697jHPTKQkumZ6Zi59IpXvGJ39rOfvTP4NQlNM4O1EIfA\nKERpIDTREbPBj/z1r3+9Uwu4ico7JuZ8schPgfnma+bbnSTM4ve61706r4jmQQ96UCoBCsozpTbh\nD0bsyP485zlPd8lLXjLb9ns3sZBIn+KgjrI6wa973euSeBBsE35t10zucIc7ZOlCxzENG4NMKryX\nTtNEgGmcidxz5d5MK2c5y1mS3JU5ZNL3TCJ1fuBpxCRMRSnVntwT2JkwrCXwC803Sdikh1uGud09\n3k456qij0iVhEmAC0yYi0/TBxKWRb9tfwKDncDfKSSZdlJn40E8y3McPa9alxSTD9kfMcv2oiNmu\ngWLamSPfgVngJDEjF0BWsnsQ8GMdr3ZDe9hJIghIABBf4YlPfOLsuqUxSszRxiYVNRCLwd+JHJDn\nahrmOBZIiEZGg1Q0AfESwVjISjUg0cjN90pDdr4wUefEJsyruWTIJEG9X8QguhdBK8RAYx6OD8jM\nxNe+kwRh00D9NRFzYhBmDUO8jqXFiQ9B0KxirHWI1ntjhuP11VhhX5OXe97znt3JT37y1mwuvVLi\nj3VB/4mJBl+tCkjGNsFTrgEB0qpplEpMwtnETlDYWkJ7R+bGIv1DQMpSjmv1k9rxLLjvH/vYx0bV\nmESthym/O+SQQ0b3a9KxP/zhD5dYC1kNwkSf99T+vhcUxsJAIVFL2fXSkn1GmGtVBDKOip53325y\nk5vk67Av7pHJhokXTD0fJhRPfepTh7ut+J7P15jfJoPaUhdbLNCulKEt3Pv48aUvLciqn/THx7MT\npXzAO/Gurd7n0JrS9yd2gcSgi337GGRXP3CBvg0tq7/pTW/ax3KVUa/CNNpHTeE+BqHRtvZGTEQM\nlOnLjajmPlYq9KFBtq839cpHGkFVPb8bny5faZDPqM0o0Zc+xbBM5Ta+a3iH26qPCUEfg3mOH0EY\no2NC4+yDCJb5l9sOrj0Ivn1MP25o2n2QYvplYyKQfuGYIPR80vzDfHZ80zGRyPsf65n7IOHsS0xY\n+ojm7vXN+9CER23zLfKNapsEufZBEn1YBhLHmJz0sPdcBXH34lxIEGIfqzHSrzuNLzLILPupf2HK\n7sOCMPUzGcTdh9aY5x3+c+187atJuF/6Aw44oI/gq4zj4e93f2JCk/gb292bmBD0QfT5HPGdv+Ql\nL+n5Xu0L75UELkGQfUxO+pjwJEYxkVuyu1iCcZ+/65k2NgN27gfsPH+hhPXhZlpyjll/mKcPWKj8\nEnGTIsJwybat/hDr5fqYOa3498Y3vnHTXSgC3jSEC9mAgflCF7pQf5e73CUDXcJsuZD9XKlTiMTA\nd7nLXa7/4Ac/2IeWkwO9bUhlXAyAsTZ/yWYDnMF21mISEJHRo2bD7JwBW6GFjrYJZBIEF2bH3oTA\noBmWiT40zLym0LCXBEKNDvzjm9Cm8vrf8Y539CYXoUn3obmO75ZYCCoy8CMNQVgwEsCJOMPUmwFg\nSLcFP4U234epedSWvpokIAkkjLjtr53jjz8+jwvTdpJwmLlHxyE15IPg1jM2IlPX1Ih81OAqb+wb\nmmX/gQ98YLRXRK73Ydbuwww72jbpjYmMyYsJkcBVgWwmGCZW+m+yNpQw5+e9a9vCP56BbZOeuzBn\n9+Gn7+3TJFwN/d3vfvf2MV8R57ggOM/2esT9CItDH1aI9Ry2oX3nScATTdDxQG6rMC8ogM3Xe8pT\nnnLZuZmGSgqBSQiIF/DcCAziYjj1qU89abeF3SbugamTT5LpmUnQEhYJHJp5eNh5SR1iwjHclLET\nw8DFJV9u4gNzIP8lk63z8iEzLz/vec/LVplqmUfdA98RcRt8smI5BFbx74779HLHP/6LiUeaF/3+\nBUIJovM3LrCwxEhQEjMpE7TPgqUsq5K7QLAU82hzS3gd+h+DkLqI3M729Ve/LEHyzDD9cmm4H+JR\nHMenrT2mY/3kJljtWsb7HOQ+vmnNz0y7zLjuMVO8Pr3yla/MJWJMuqsJN8ErXvGKjJtx7XASJ8EM\nD9vxRCDcHEN8uB48f8y+488e03NMrtI90frgmR3GANje7pP7Qvjx+aYj0j4/T/uPyX9PyPiUISLv\n+vAVjG/e8s9mUltp3i4NeMtvYZ1gkwhYemHZDI1lJfEbGZpV7RsRzEtM2Csdu5Htj33sY3uaUvhi\n05RKWzjHOc6Ry74st4mgrI00u+Fj3vOe9/QxIU+TMG0rfIy5nChIM7XZZsrnlmAZCF/kxHMFoaSp\n01KqCHxLkydtOoi9D1LpLecJAsjlUTGZSI1+aA2Y2OgMN9I0Wf70b6h1bvQU3DNXCdcF10KTIOAl\nFgKWA9o+zX1cjj322D4CA5dsZsambQ/Fcq7ww6ebgHUqMpr14Qcf7rJw7+epAe8DjbVmGnFjMpDC\nLHirREBJmBFz1jlt0NV6+iKrl8X7ZsolhcBORYCmZsmQNIe0N5pjEFFmrduqa5JBy9Ia2g3NjDbl\ns+hUWtN2i8QMAr5Of/rTdzEZGJ1eQJVgJZm14CSIkwa+kgiUovGJfKat09QE/9B2icjnIPwMJrIc\nZhhctlKbi7xdMJmlTQLuBKO5fpaEmGSllizYyTLUJzzhCcsuA02EkpTWGeM0i4tgKUu/RIwPRUCX\npC5eRcIvugVTALAo+LUC0IbXOKv3ywgY0H7UMskI6SceRNGTtstSsxOlCHgn3rXq8yQETFaPibSR\niFCkMFNxyR8QsIwL+So0MW5GnYSRpUuyg1EymKUtcdrNYkkT9wazu7FchLulZZb5+DzJ/N/wEM3O\nlCyymyk+LAyjaPK2z058XSgCFqZuDZ0wfCHshJ/A2j6h/lLPte07Cewi4J10t6qvhUAhUAhsDwLz\nJOBlQVjWrlm4PQwgYKaQMCB8EUnOO5GAt+dW1lkKgUKgECgECoHpEDjRcDeaLhOF6LhJwkSzUxN8\nT7qe2lYIFAKFQCFQCMwLgSUETNMVaDBMATfsmO2c6iWFQCFQCBQChUAhsDkElhCwpjjWre/iqG/C\n+R4LuTMoS8q5kkKgECgECoFCoBDYHALLfMBCzGNtYWq6lhgIIZcfVtScMPZp8plurkt1dCFQCBQC\nhUAhsPsRWEbALtnaLplMVCSxXuziF794rv9ryeJ3Pyx1hYXAYiKgApFlI7JQyRYkM1Skpuyijm4W\nc7BeVWaotUTBE5mNIhVmZhFT8UjhBOthFRyQkWkoMkg5h6xKqiGpRjStyFJmdYUiL4pPWHc6TVGD\n1r7CENbnakeWMCs09HMtEc9iRQeFQvxKJKJYcgirnsINlnVZzhXJN0YFEJbsuM4PMknpr3atq4XX\nThGFGhRQgLVylIpRbEVehlnioa8ycsFb5SoFQ3aKLDNBt45LZSZ1mwoc3vvxeZBLCoFCYG0EIiF9\nrtWVTnClCl1rt7J0DylblZvbf//9uyg2nysTJBBAnkjXgGkdq+o+q4k1r9IWsnBFhqPuiU98Ylar\nUU1M2klraFVLatLq51oJYTwwyKmgs5KYHEj2oDqRZBhIU9IH50PytnFlySswTIUY+YLTyiahRhMV\niKS+tK/3Bldl/eC7mlirypXmfMYxBDxMm4hYkK9+Sjkp74FJwjSiqpBUm5ZkutahmCApeYh49ROZ\n6cd6JPJiZ1pS+KnaNLwX62lnvfvqexSdyD8pLU2S1ERGbIsq1n1HQY9cxy1+Sb6Khz3sYYva3eX9\nkglrKNKLSegdJaRysyonMdvsJSmXDH0WadGG59uu95WKcruQrvMEqWRKP4UDVJdROCA01VGRgI0i\npOiB4gVN/BYl25eGsYk0gs4VxNA2LXuNyXQWMPCF1IExwc5jgih76SUVK5DGUZpLqR8j41ZW0GkN\nKUigKlFo0VnJKAgy0xRGLutMQWiciElCpouMEaeP/O59ZM3qI690HyUPs/pTuLR6aW9955xR/jSL\nIATZ5z6tIEOQUB8aZTt1vioGoWLTUKSJ1L4/RRcUWZA+M8i1D0048bjxjW+c7yOTVo5lMaHJhP+R\nOSuLF0jpqThGExWVpKRU7CESUGRFIUUJpFdUPMYY6frc3whO7SOTVBaTGC88AEuYTyOKiagAJCUp\nUYjBfd+O9MAxUVhSfMP5IytWVrryfhEFtsPUrH57nqv1pA2dZyrKZRqw2ZpIZ0nYZdphjjaDZ5qQ\n5u2II45YzuK1pRDYgQhIp8cM6xmnBQ61sc1cjtSGNCAald+MdIZnPetZu9e85jWbaTaPHa7BV8TB\nb5VG28T6fbW8ZXhaSaQIbBmfZEJibpZ+kbYoKQFtkAYkeb+Ul7QM5tkYgLNJBee9Z1q9/e1vn2kw\naYQyT9H41OmFqTb1RZYlmZNom7QsfVY4Ax5BilmXWFpLmhbtT51ZJlypDmm6tFUuMffItTqPsakJ\nzV1faIvOJU5F3IriDIraNy1YvWPmYUUVWPNkfWI9kPHPeWEnYQ989IXmzlKgBjG8aO5M7xISqXEr\nra02xMlEybxO/d0g6GXmeebt1e4HN4DgV5qc62Cihw+R5lGRDvE3TeDr/OJ1mONnJbBr521tSne6\nyBowawRLQRNuUr857oedIEsI2I9K2kmDkh+EfJ5ePXiE2WhoHtoJF1h9LAQmIWAAVpBeXuVIMp9F\n3Q3Uw4F90nHTbDMIx6x6ya4G+s0OCkicmbYJcrNawcRBrAZBln63zMgrCRJX9F2FG6ZaBGx9vwGY\nCdKgi/iQBl+x/aM8XmbD0yay4ZJCvs7HHK4NJkDv9QspIonmK95vv/3SX60tPmw4M5/LP8yHjbAR\nkXMjfeQcJQbTdM13zOwdBQUyR4H8zm0iIi90lE3MpZP3uMc90jfM1M1txmzNz4uMVVljyj788MPz\nXocWm/5oPnQkHbV2E1vn4XPWB5We9NFz4VrlCpY7GimKjzHQq1RE5JlXxQhZmXA1MaY6r+fMhM+1\nq+LEHK5SEeKHOdOp/fST8uNeNJHzurn/PFvImkndcY7hlpiFuHaTnSaeAeewfVEFPw1X7OinyYpn\ncCfIEgI2u/RjbgEYfmTDYAkP+3rKce0EAKqPexOBI488MpPO3/GOd0ziMNjSKORY3qz4jbAYDcVA\na7DYjNBCBRIZ9E2U9deATWs1KNPYaKfOj3hWEhMPlizaHRwM9gaxj33sY1lkAdFpAykb8L038UZK\nUV0oyYjmyg+MMGm1/KEmB8YQ1ylwJ6ooJakqo4e0+VyRoUAsEwbaC9JExlH5JzU/ATWEFt4GUROX\nqEWc5NVIwRgVZur0USI5pOz6WR5MAuBgLHvqU5+axMd/rtSgbH7ORRt3Tfro2g899NCclPiMRPWt\n5dhmAYQvzLVDYOa6+cRdO1860qedKwaB1PnTTbzcMxMQ+yJS56fpwsP3iJ3WTpN2HpYNwWMEaSu3\n2VafNGuNAhzun3skMM65NivwdI38vjRr/WURGA9e2+x5Znm8ia5ymOIDvvCFL+Qz4RnaKctll0RB\nS8ThIZX3WdUMKSnN1oiH3E1hTikpBHY6AiaTBsqhGOSGGubwu/W8N5AxJzJJGlwRFZOuCj4IxO8I\nESEqZtZpInqdn4aJmGh2NLBmukQUBkoBQRLq07IEoiA6FWyaMMkKCkN+Bm2BW5Lr0zZpwwSB0p4V\nNKChIdgojp7tH3XUUdmeCkS0UuOFcyIrkwLBQo5XKYmpVy1bFdSMHUy4vtcHhOscSMN3JhHw8BfF\n4JPoac/ad49o0wbY4447LkkSUTUTNu0Xxmr4MgcjMMSNuFyra3Mf5DJgWnZdUXIvr5tlD7EjRRol\nE7VnACHT/B3rnLRMEyikCTf1jp0f+ZmcMJnrn+txTz1bxk3HOoaWzezOPG8yARv3kbuPJm7iY199\nYGp3/5ihPS+eRxHoxuUmVqUMRdurmbiH+672Hk7uq+cVicF20cd7kxD4sD6wxngWTLp2jMQPYImo\n3SgYQWBGPMx9PLh9/CgyqEIgVswOl+y/Uz7EzLGPGd1O6W71c4sRiMGwF/AzlFjCk7Vgh9umfR+a\nUR/myl4bApBi0O5jZt6HltrHYJo1Z4OcMlgnBrY+tK8+fJoZxBPENO1pRvsFWfVBOPk5Zv59DJT5\nPjS5XvBQEH0GSgUR5fYgmT7II4OS/J6DUPow1fahxfVB5tkPgVFBIBkkFRpkjgExkGX939BU+yCH\nPki1DzLtg7z7MGNnQJJ9bHeMsSMIMNsLAs1XgVcC0gSMBWH14afrg8D60FTzOMfrmzbUkvUqYMr2\nIOI+NMI+Jg15Hc4h6Ck03bw+n4MAc1+4h/mxDyLJfuinIKoYpPN77QnQUVM5yipm8FdYA7JfAp1C\nS+2DdPM8QdZ9EF32NzTgPEZwG1z1PSYNeX59hUtoqYmT4yaJQDMioMsYS8LVl3WV3cfwQ+c2xwuG\nCw0671EQdm5v/8Ik3Id1o33M4LiYmGXg2WhjvVkXAvMMwjIDnSgxAxptj5lFH2aWjAIcbdxhb4qA\nd9gN2+LuhhaWheYRZGgvGcEaQTw54VzvqUPjyQE+NIc8VHRwaMB9+9zaUxx+fBIYWmVG7rZ9pn2N\nQJwcvO0fGlSPIEmY3pKAvQ9T4iiaNkzsGclrexMEI9o4zMMZNRxm6bwOEcShSYxIC4HZV+TvS17y\nkiTY8Nsm4ThfaLN9aLp9mIUzghmZITsEHNpzEpTjrxIF4e2H5EMLTAJD2KJ+7a8d5B2+7vyM5BFy\nmIX7WPOc3yNw+4YJOS9DNHYsM8poXSQegV9JciYkiB5Be4+cFbenQLgekw3R2rFkqA9LX/6FWXdJ\nMfowv2fbsBNpSxkhCN9ki3iOQhPOaHDbVxL9FD0eloqcuNjPNcEnNPrsN2xN4EQeryRWqbh+E0hj\nMvxNMko2jsA8CXiJD5gphi+DMK004c+x/o6JoolAD6amkkJgJyLAh8jXGUvu0l/Ld8iMGBrNui+H\neVKEbvM7yRrHx9r8eK1BJli+xqEwH/NLrlcEBvGtMmHzWzKtMtcy8QrWYkrk4wwCyqaZVCXuGAr/\nt4htAUT6xows4pbfN4az3FWgkQhnr37vInCZlY0P9mNiFWhlG18cE6v6usyohDmT75gPmG+V/5kp\nnak1tMYMatJ/5mY+XJgx34s05gtlYmRGF+nKx8pcz/dtrTNzN5+rPjA3M81rk2leBDczqvNbB2xN\nLr81c7f7rM/M4szqN7/5zfOPn1YfmzC1a1/Alz55NgStMTUzuzOZe458z9zvu5WErxve7gGcxNYw\n7+sj87EgLCZyZl++/pVEn5hamdTl5rc2Owh7pd1r+4IjsMQHjGCPC1+ESDg+YD86vpomfuRu+tOf\n/vT0owjgKCkEdioCliwY+DYrAnJawFBrC1EYKIciElZgYyNq35nIGlTXK8gAsSEXgUF8yyYCBmPb\nTaSRHmIkoncFUIngbaIvyACZIRq+T0T1+c9/PskFNnypCJUgKEur+FqRIFLh1zQREPA0TIBgEmA7\nMpSdC1HxT4v+5cMVgBQacfo2W5wJ0uVvFXFtQsOfyteKMLXFzyc+JbTp9KMiUW07r/YFNPm++U5d\nO/+odiTH8Oc6nd9EJbTiJH7X5j7wzQ/JzDktUbI8yUTFOYyNopxNUFSNk8QD+bqehpP2xoUfWKIU\ny6v0B3lrg//SpIX/eVqhEAm8K9kFCExS3PmIYraWPiImIeYbpiC+D2atWDs46bCF3lYm6IW+PTu6\nc/yxoQWlWbVdiOdt3JTIB8zc6i8mun1obX0E3mzatcOPK3EDEyf/INN3aGitK6PXINc0x/JzShrB\nJNzMqnbit2bCDZJK365tfMcxEU+zZ2jYacaVHIOJmq+SGTUm4mlGDbJLfzI/bAQzpZ82hsj+mGOO\n6YMY+yCs9H8GeeR4wlStbaZn+8Vym/TLxkQgP2tfIoqhwM65JRqJAKU0HTNpx1KZngmZ333oPmvH\nhhafJvIg6zQ789uKc5G4w32SXCMsIm33Ja+hofYRRNfHsqiRL9oOzOiuLdYDZ0KTJQfVhx2DwDxN\n0PtAadI8gjnajI95ygyNSYf5aKeKKFHXYvF8SSEwawRonJa/WDdpeQqzamRimngaWiANiHWJWXJo\nZZp4wAw30pJpiNaWMsmyAowLjV5SC1qs373lHTTSleqEO572yOxMq6ThiWZmsraNyZaJmdm1afvM\nxTRaEcU0baZ0UcXM6EyxtDxrlWmOkY0vu2h/GrJ9aaqWHtHaabW0/rXE719KTHhzPRjjRHizHkga\nQkMt2XsIsCZY7y2CertlRQJGWPxHssDsBikC3g13cbGvgS8PsfIB813udLHUCUm5lmFMyErXxRxr\n6SKytbyGL5MZdyWBl+U2/KCW2SBSxMwV5njLuUxqTASQJh8wk7f3JgWhgSZptqQcK52nthcCqyEw\nTwJe4gMedlKAghmpQIdJs+ThvvW+ECgEuvQt8i/uFlmvRsAv7G9agZUEKEMRezIUiSGsW+Zj5oNu\nY1EsI8oKbcN9630hsNMQWJGAmZ8txDfzFTzSHnzR0GahJYVAIVAIbAcClIGSQmA3IrAiAUeww5Ls\nK+3i5VktKQQKgUKgECgECoHNIbAiAZt1tpmn4AUBCnw7JYVAIVAIFAKFQCGweQSWJOIYNmehtzVw\n1tyJXhTJKEJR4ERJIVAIFAKFQCFQCGwOgRUJ2IJxywAsFCeWJVhCYHtJIVAIrA8BS10kuLBEaTeJ\n67K0R0RySSFQCKwPgRUJWGYY6+0sDSCyykRygSTl9Z2i9i4E9jYC1sNKkSg9pUxTyr3JnrSWSG3o\nNygVY6s7qzqO6jtSMwqInEc6WGkYZcESlWzN75WudKXMsCVjlPXAgjRVGZJtirCesaSJehbUKXUk\n0paWU7UdS41WyiIlnaayeK7VuuVp0nbCRMk/a56tKZZe8vDDD0/ctCWd5lC0CU/LnSy9LCVjiM7i\nvjfpk0pURS9R8jtSVkpXIsF3rAHOjDNRvit3U72lJSFf6bhF3V6ZsBb1zuzOfsmeJMuSCmIxMGTh\nAon4ZZ5SVUeFpNVEgQVZsiJdZBYCiFUJfeR/zuxTqhDF4JMVemSLktUpyG7F5hRTkeg/Uj5mpqq2\noz5GWbz2cdlrlAHsI71jZsxSwUkhCRWMVBtyTRETksUcFEGI9b5Z0ch2BRYiZiT3CZLOV5n0ZLoK\nK1pWErKfgggxsc9MWJEYI7NstU7I5BUk2sf64Cx2EJp2VgdSMCMIs+227FVhhMivnZWmYklU9sl5\nIylKXmvkyM7sXbJtEe3qgwxgkWKyj4QeWSwiStota3ulDSo1ffGLX8zKRIozyAwWpQb7mDz1CnWs\nV1y78SpSd/YxueljArPeJnbl/gpRyEYmo1vEJ+Vz5TnyflL2s2lBmGcmrBWrIUXgVf6Q/DCULYvf\nvdcAAEAASURBVFNRJGaIfdQNnfa6Fmq/IuCFuh3LOmOgijzDWcmmTfyW7bQAG5SSa0Skqk6sU13W\nK4OwNIfI0e8G+SCtRjbINYoeLDtuuEFaR2UGQ5tL4pVqEclJuyg9bGiS+d7goaKPgSiSWGR6S2Qr\n7SWBqzSZoUH2oYVnqb8oPpADu3SR0jciH312bSbZkes9yR+JOp/fv/b9qWrkFclKZym9pG2IWf98\np0SfsQJBt8+RizrbNXjaZl9kjKjs5zO8DKQmCnDTrrKD0k8q00eU45M2UqlUg3GT0ICyKpS2jVGR\nsz6J1rXrvwlMK/uI0KSzhIlSia7ThEglIqUKTShUUVIGUdlIaT6bhGbfS6GpCpEyjsYVkwTX6/6G\nlp9lLqUnNYGAbSul2NpY7dV1mjCowBRWkjzW9e91EpYeOZbC5rPjfqk2pmRjWFJWg3PN70xkwyKT\nz86aO2/BDisSsJJqaonK4Roqfj4ASnlFWsot6MbWN1kEvPUYb/QMBh2kEgnvewMXzUuO4dW0s42e\na63jPPNKz8l3bHCmwZqE0haRoQGeFkX8eGlkUXBgSbN+L2E2zkHa/v7kUEdsiFMZPG2uJgZ5gmy8\n93vUn6igk7V4EZN+IBLnQ9AIy+/1KpHj2TngSgP1OQrWp6aMJNSydRzSQJyIzyTBpCGyTCWB6rPP\n/rxXcxaJIjIavP1how15lpH5kIAd4556dU4lDsMHnnV4YaBdkxLXpN02uPrsGPh5VXLPAKn8oLKB\nJiZKKGrLhEIJRffGPnBSwhCRal/JRIO0bSx3CJfQKpH/Rz7ykWyDJk5rbpMW53Q84jNBcI0mhwZ9\n5Cx/NQz0D3YmA8ZGNYzh4h408SyxfEwrnn1j1VDkqDZp2u3iPspl7vpNbobCcgRLloth/vLhPmu9\nd4+i8Egf6VGzzrTJp+fCfTUpnocsS0UpqEIEtDRy1gKrYNIkkqxnNZO3ve1tbdOOea1UlIt7q1TX\nUg5PWsImfDsClvjutkuCULMKGB9hkEkXE4AuiCWzwfFfqqzD76mqThOBijFgd8PKYJ61IMMuih6k\njzSKl6SPVC51v6EYaNIXqlLQShLkkr8/Zfv4R6Vq5D+VotHxQQpZai8G/FydoGpRDCCZv13ApPzJ\nfLX8sEotuhYlDB2nupAKRL6XX5nfU0UkyXeCtNOf5vq9V21IQh7pNaWAdJ9kx1ONKcgo/atBmhmE\nZVuQbhdad37n+Obr1ra0lvobhRQyraRrd25V14J4si37GXtUaVICkM/b8+F65JdWolD+aOcM11hu\nD6LNXNA+w/6EqA4lcRD/sQpJn/jEJzIntdSWcIR7mC3zPd+669Fv91j2P3mBY8LS3fKWt8w+w4xP\nG77KRwY5Z7lHFa9cE4z1Wz9hCyPtEH2RE9zzPI2E9SJzU/Ona889gj3MtL2bRLUwvx951L2G5SIx\ndr1w4PNfr/jtyg/udyKnuWej/VlOK1e5ymD+lMX0TC9UKkoPih89UXprKIAZlusaflfvC4GNImDA\nNqgORRpExLVdYuIpmEhAkEFeHmQ/ZgFFBmf5ikUxI7OhCELyQx+KwEVkrl6uOrxK6ilnZ9A3WCMd\npfRWEgM9MhCkhOT0y/4KIxiQDVQCjQQUCcgyYVZbVgCU+rDSN4aZLvNSIyIDHYyVJ1TMQICS37L9\nwyScZOw8iEZ/5WJG2I412da+gcqf98qSIlv99Nl1NmlBUjAIv2jbnETlGAFRBOkRZBYaY76aYLgP\nxiADsHSTrteEx7H+bAvNJQnR+GRADfN54mM/iYIQuhrGBmHERZF4wAMekLWAYSOfgZKCbQCGjfsS\n2mwWnNBHRKt8o3NZCaKf+mxSiPzdD6VZ9Sk04EzBaYLjmfG8NDF5MRGRI1vOavdwKPpnuWdYM/La\n9dUxzueeEvcNzvplArNRMTGIqk6Jl+A3gWfbKZ5D1xKVwBJDJRxNKkxk1ElW5tLkMaxDU+WccN9N\ndGCnqIbJmntJTHaNKe4xslXUA55wXSiJH9Ey4XvgEwmw0g/hMx9LzPbKBL0MrdqwWQSiOlCaR4ft\n8LPyaW6XcK3EAJDmTSbKFtRx5zvfuQ/tK82RoY2naTwGzeyW3wST4+tf//ol3WTqYppsvtMYYNL0\nHKSUZlImr4i0TdOp35mARxg08ZlJmYmVKTm0qzxPDOxLAqB8jsEkzeV8j96HRpv+T34yn/0FSWTA\nU3vPjBpRzGnOjYEqzb/2Yap1XubiGKhGx7d2HOc9H6VX+7T3bZ9pXodte88H3EzQ+qGN4avrb+0q\niQpz5m6mbdtjEpJ+WGZ+5Qb5pbVnP2ZyrozIZZAm4v3CJA8r5m/Xw4fOJK8dft0g+F7ZRZ+jolW6\nCoKcsxSrbc4bhNoLStOGbfy1+uD5sc39DhLto75x+pLFNIQ2m/tGZHa7zWnyFuDqe89SkEeaRJ1X\nu+IEouJTmte5HGKyNDp2vW/4swV1ee70DTb6vZWCN5STdH184e0ew51ZXsxBrLYZ+ffX6ovfqLKQ\n4gDgNnyO4NX+YnKZsRBrtde+X6ggLA8XonXj+Xa8b3/qXvJ/7EQpH/Di3jWDj8HGn1q2CMiAExrH\nmp0WuWrAvGpEDEci//TFrXnQhB1CO0gf4UMe8pBsJ8yPuZd+GNj9uEVhCsLhPxRVazvCG5eYjWdN\nXf5aflkEYuAW0MSXyoeJ4Pkdo4JQDkJIX/9Dc05SE0jF38VXbLBsA3sjHq+IQx/UFUYq2g+tOYO2\n9BeJtUHP50Y0SLORqe0IcPjZNn+NYNrn8VfHNBJ0rvHz2X9IngZM+xggh23ZNvw8zXs+eufXd9cF\na+/VNDbg80kjQufirw1Tcx/m4MQSibdz8NuaGNnm+NDy00dsG4xNttx3+zcs3VMTF9fTtgnEcp+M\nj4LDREIj/7AyjB4PgUShleU9tvEDH/jAslUlfP3uI988fygC8/vgV1aXfaPCny16vklYbXLSMB6/\n0L6fxasJNNw8I55vkyN9wCdriaBA5AxHE6PVJnruPT88jPj9w1qwVvNLvl8oAhaB2B7O8VcPs6CG\nnShFwIt/1wRZmJUbwCwPWUsUZBd4E2a/nEWHyTAHWz/ejYhz+yELUDLIChZCtgYQATtNnC/MaPlj\nb9vaq/1oGgKfBJSFCbtH5qJpBRaZXBCz+HHN2bIZQUYGaYN+E4M6ktIvA5kgoRY8JWrXRMVv059A\nI8SBTByDKAx8TRsX3et3jXAEKzVtEZGME2HTMFw/QgoTeuLSxgVkhyza59ZW++x12CZCb/0Y7rPa\ne32wNKhNHuyLeJHb7W9/+7xORGu7V8umYOz5YWmASZg6e+QHW/vB0XPjT1v6BFeTBXjZx6TGK4zg\n73nw2T6tL15NkCxZMjETONisI+6dCRbyHApCCZN2bnIfWVXGxT0y8WtiGZl76po3Kp6pcWKilcNm\no0JZYyV95CMfmRMJk4eh+Ox3MsRk+P3wvUhxCh7Fz2SmTWxgPvxzj022BR6yJoSLYtjMht4vFAG7\nAqYDD2DY1peYoDd0dQtyUBHwgtyIGXbDzFg07FCQjUjSjUr4FdPcjEwMeAiZVjqt0Mz0yRpgS3oI\nc5tB1+BueQwRfcksOBRRvgYfM3kmtjYJQeYGIRHCbRDVJySKGEwIDPaIohFwM0EbyDz7jViQBtO2\nAdlyHQRjIG7LnGiAzmU/ZlWfEQsCaH80Pe3Sutv+jkG2rBjDAbNNBBxj8ER+w++Reuub7TQdGAz3\nsdypadq2I0EmTSSFVH3WN5YQmMDRAA03kxp/8HYuZkxR146hGbtObVtWpY+I2kSOlcK6a+3CSt+R\nufMjXaRtm88IMuIV0mQ9vJ/ux/g9ZqEIv2fuxjSubVpbE5YPEzi46r/nsUXr6u9GhXVlPLJYhD0C\nXY+IFuY20W8Yun6TJMvGmOqnEdq35XuwcB+b+0Rb439cBiLcmc6ZrKexik3Th+E+8yTgk8QFL5P4\n0XTRqWXba0MhsEgICIqJwXtJl2IAzsCbJRvX8UGkrL+NShBTF77UjOQNEs+AJQE+oSV0YRrNSGpt\n63eYIDOQqp3rmGOOyXSvMdDn9pgAZDS1YB8R2KKABRFpP3yQGdwT/sIMWAlyyeAuQVMwsG8QRAbc\niOAV3BRkkoE3ApwE/gjIicGzi0Eug1UEXgkWE30rWEYwjCAZwVQCiUQUiyAWaBWEnVHGApIEqJEY\n1JZkyguNNyO0Y0KfgV8x0ObxxpfQDPMYAV1BuvneP23FwJ7BTdojRx999CiaOkg+9xfwFNpVBopp\nS8nUsFbkvRP1KuBGX/UzCDjbEVUNB1Gyrlk2LsfojwhZEdSh6WdgG2wE9mhX0FsQYgZhxeSgi2VB\nGdAl8hxWot1FU4f7JM/T/jmvgFbBYkHYGQ2trRb85BmI5VUZJOR+CDjTDxHYgr0EEAlMi0lC/k0b\nSd3OP3wV6RuTn4zYd81WHMBAoNq04t4IJCMx8UtcrZIRsBaWkBWbac+tYCnPvODKdv+HB7nvnrnQ\ncLsDDzwws6QNn43hvrvm/XAm4L0ZJbOBdXeCAcb/mAh2opQGvBPv2up9tjZTtqEm1vCajZspz0sE\n57AeERosHy8tahhk5TuaVgwiufaZ2ZopmcbU/I1M1zR5ZlIBUzRrmhuN1dpj2py1vTR1QmNjEuY3\no6Fom0ZKI/QKFxqUY2nHtC6aZtNIaa7MzHyljpXAwisNVv8FfMkyRTO3nYYWhLBEe2GupxnqZzu/\nbTRpn5l7vdIk+TNbEBlNUv98N+mvmYlp3frT2tL3IJHUVGnJrgGGsdQrnwsaXrMYwMi45vppq9Z0\nw5D2S+tmQm770hT5TAltjZ+fNaQl1KDpWU8qQI7Ljp/X/ZwkAp5otILAaOWT3CP6EhOnzHrWrB7a\nYl7lJ2Y1mYXmp//GQYGF7t14mz67ds8va4K+j0ss6Vo1ExmztOeZWZ4LoLk8Jt1XFgfJbGDIFz1u\nrh8/9/CzeyVRDWsHM77EURuVeWrAy9YBt9mhkHEz4nGJH02uJxzfvuifzW7NLsPPsOhdrf5NiUAE\nc+TyBUtTwpSVS08icUIXSQumbGH2u9ESaL6WVMTgkstPrCuNCNZlJ7OsJAa7XPoTxJY5kmnQtgdx\npyZPI7AUJvxouT7V0o3wV+ZyDdow7ZYWbClUkE9qvTRdS2r8hmkflurc8Y53zHzuNFbrY8N/mloG\nbYRWyJpA447Any7ILDUu2goNKQa61IKtP6ad+x3RammH+qrPlrg43nbjBi1bu+EmSE2LNmwf2hcN\nWoW1IObUEGmSQ42IVh4D7AgvGr17HSbnxMXyK0u5aF20SGuwndN7S4ZcM43Tc6BvQ7G8jNbpfJbi\nBCHl9dK0bhv3KLJepbXC0ijPVROWAWOIHPnuheWY1vdaJ76ThQUCZtbiut+0cOIZDhLNZ2q167Mc\njmbrj9XEmmvPwLjEJCo18DCr53NHw7VUbj1iDb31wu4hnvLsEW1bVuZ3sRGZ5zrgZQS8kQvYCccU\nAe+Eu7T+PhqoJarwY0R4yGbeYgAyqOkTAkVMsxLmYAMlkg3tONfuDttGZgQBrSbWUDKNM60iVetX\nEQuTJzOp9g2WXscFeSHY8KfmQB0+uhwAkRMzYvj2knQdhzgNmIiQCRQR22aiZPBmXrU/cysiZW4n\nCDosHFnIgamYydMabYOtSY5JglcKgYIVjt+MWB8tGYn+MBtPao9pGFEx7SN3z9tOF8kuEBuTPnNy\n+2OKHxfPNeJDttbcIlz3cJKYNCFEf8jW/WPqX0s8g2HByt/xuFkbYZvU+T1xLbQ/9yosGWs1veL3\nC0XAZnRmiH4IfFKTxIJ9Ny7M0ZO+XshtRcALeVuqU4VAIbCFCEQkfk4aTBxMLmj2QzFhMxljzRgX\nFoum3Zr0mUghwHExqUKGQ+2WhWItYaHBM7Rmf9rXX5PqWA6YcQrDNkzcTMDEAcxS5knAy6YksXYr\nZ0NtRjTpQpmQkC9TELNPSSFQCBQChcD8EeCKEBCGcP0xxxOm/2EK1dZTlhJ/XBDcEQhX8BlrBvP0\nJOHeGGq3NNK1NFBtIdhGttwaNNzwF+cpwh+fJM5dg8xlxBoX1pXdJssImJmIAEe05UrC/GPmU1II\nFAKFQCEwHwRESzey5ToQeR1BVumaEE3cTMriBIZCiUJ+4giYkmN50bKUqvZHrMzHLTKZhRQBTyMR\nFJVKGr+t8xH+fb510dSxxC+3IVyuhL0oywh4WhAEmZQUAoVAIVAIbC8CfLb80cfFMix+eGKJF63R\nUqtYC75EeWLSpd0iW75b2m1ERE/sNItm026RLXJcSdHiE7bki1bLNxxrjZcFpYkhiIjqbIdyh8z5\n0Ev+gMCGCbgALAQKgUKgENheBATAMSUjRT5XUdy0XAUHhr5RxSiYk5Gt4DL+03ERFCX6nnaLbAVL\nCZ5aTQQ8ipRHujTu5hMWyIestdNEfyKrXftYrxMQKAKeAEptKgREMDPLmcGLZG4+Lr6ySIGXS4dE\nwW4kEtaAqGoLvxeTHI2Aj24lMchJsGGJDA3CYOv4FuiiIozgFMt0VtJWtEEDklCD+c85BeC0KOiV\nzj3cbhmSQXuSuZCJUaTzpO+GbbT3NDdaGP+jaxoX/WVejbWi2a7BfHzZCq0OLq5BFShuMQThGmlx\nknE08Z3zifLeLxJQrCZMsrDWN9WJtlMEPtFsmZX14053ulOSbOsD/Pl1ER5MaLe0T4FE8LDEzLVO\nEvipOmRpGbL1XE+KchcdL4kJU7OyiEOJVMRpuka2Alu90mxVeRpOAIbH1PuVESgCXhmb+maPImDw\ntRRF1iPLLJSSM2hZ/2qQYeoTpGgwk+XI+tHVhKkOmSA9ayu1aXCL3NO5FtX3iFyN3rZu1QDYSMoa\nVASHrEWOIpxIOpFZjSwXMYgqI+gczIAnnHBC1gzWL8t9fM8vaGAVZRppLHO5kHWwTJL6ZR/+w0j0\nkeehQSEB10tL0r41okoP0qYQhehZ/TVIm0Bo20TAuSLdZV6f9rUR+ZkzYxKclPmLvN9JAF4tOYp8\nz7nG0/paBOM8zKpKQyIZ5xHFK8DIZEimKmUVEQAzqKBQ5GpS4twIwfePeMQj8noFJ9EYLbeSuYnm\nCHf3eEhCtsPJvpFKNKOG1SY26TL54kvVFzEyTL2zEPdadDK8LbkirsUzhySHglz5bpt2a1Ll2sbF\ns9K0W2Trz4RvXNxD5x0GSHl+iHXlJjhDGc/2Nfyu3m8AgY1mD9lpx8UPq1firqQQGEdA9h5ZgkIj\nzExFoUVmknrbYyDMrEBBTpkoPgayzEurjRgMMydumOPGmxx9DjLJMnUKMuwXWZtiUMyyc/FT7eX9\n9Vku5ogkzf3k7I1lfplnN7ScJZmhZMNynD/7tPcyX8WgOcp4FdGimXUqBuHcLwg2qzDJfCX5vuOC\nzEavoVWN8hoHWY7aCaIbncMx+jbep9YHr7JyxXKWzIbl3LE+MwspxEQgs2npR2iV2WZoT5nnODTd\nzE4l37Q27OPVsa1tfXUffHZv2j6hOY+uw3YZuGQ1kjNbhjT7t/PJCOaz6kfteu2nn5FaMu+XfN0y\n/w1FzuMg28zf3NqMSU22I/+2Z2QzIrtYmIDzfsnjfcQRR2SWrTA1Z2auIOTMtOWc+tYwGX+NiU9e\nl4xqsJMrfCgxicmsXsNt3itcoS04KMVojFQwQpWxmOyN774rPy9UJqy4GbtSah3wrrytm7ooGo1l\nd/xUTJ1MrLQa5k+mNqZAM/5IC5kFvWl+kRS+i0pGWTTdyeXnpaHJNNXkfe97X3f44Ydn9iiaYgyw\naQ6VV5l5VHYoa+lps3xpkmvI5ERTjBEum6FhteLirV2vw320QVNyvDZpaXyEbR9a9jBRAs2R1uc1\nBtzsS2u7HdM+e6WB0ny1GaSXiUVa/4b7tfe0YO27Zu0xl/pMaI2OhRWhhVqaov3WJu3Zn/vABWBf\nbXht79v16b8EHjClxemf87pmn2mF/iL9ZhcTn8zZTONnrnf92tNf2p7zW3cqCQStU4Yuog8idmno\nUckq+0zLd/9prPJ7yyzG/LuSsBowJTezsmdOogniGWNpEDhFo/XcRNrLtLjIN80S41rGxbXTZuHk\net135nbtsYKwFDA3M1N7vmi3tGzLeIbPg3Zp+5YEscD4DawmzS0DP26Mldwdq7WxiN8t1DrgRQSo\n+lQIbBYBg7FMSwY6Ay5To1SCPkeO3jR/8kVGicBRqlXH8AMarJmfLcvjN0UaTfjdmCWZKfniDLjI\n1AApwf4xkcxGsgEEwaypLdsQJ9OnvtifuTCqKCXpGVgRtQHRoEcaeTay8p1+KJoibaWoWANzEwQ4\nPtg2MmyvbV+vrd3hNteqv8RkQZuI1LW0z8Pj2ppT+9vuPPqkDcTjPUJFokzTTLwyUPHNul6Y2Mf3\n7bzeIw6TH+9b29qLcn5pcteG/hCEIpK3TV7so23mdeZc5ltme9fAnOsZ4ApQVAFxRf7t9KW678zg\n9mPW5ltFuhJW6KP1qto1QXOdzsstICDKud17y28QHyyQlXSpJg3ERMAzw/Tu+RAsxTUgt8K4cDkI\nbmq+W75+zyk8mOQRtXMhW0RvUgEfov/M7Pob2vx401nYgnl6LXGP+NkRL9xM+ExGdn2xhLWA2ez3\n8XDsCSkT9J64zRMvMgbzLC7A7BkDdR8DXSaBV8i7FU5wIFOpIuJMcWoDh0aVZf5iyV2anz1DzLuS\n9yswEP7KNIHGgN8H4WbieeXVYsDMdkKj6Zms7auoAlMXk2hoXln6zrb4/WZBBmZOZsQYMEcFB3w3\nzV8QwpL9giRHZtrx4/V/fJvPQfBpeh7/Tlvj29pn19ner/YaxJ37eR22FxOQ0fHhU0/z8vi1TGqX\nObm12UzMbb9mqm6fx89hu/sHB+cKUss+MJ0zgzNjuw+KXgSJ5neuMwgwiwsojOE45mIFILQfgWf5\nWdtBqmlCdj+1x2wc8QSjttSBduxK90Ebri+07iyqcdUwTzNDDyUIOws8hJabfWnXGpOyNJfbrqa2\n44KIh4du6H1o4fl8KBjRRLGFCBCbSfutzXm9ztMEbXa2J6QIeE/c5okX+d73vreP3L1LvlPnl89S\ntaImCNOPkZ9Q5SA+PoOowT60pz6CjXIgNkAalA3kapUaLPnSDMSNZAzkCNygGKbc3DfMhUnAfJBt\nv/a+EYX9Dai2t4F10iuf50pkNX5s+7zS/pPab0Q5PEafWz8nHbPebcO2Xc+0x4+Tbjtu2F7b5tV9\nap9dQ2i0OXEyaRrij4TdKz5nJBaR1KPqT6G5JjFrhy9cpZ/WpmclTMlZB9r9U0VIjWb323d8siv1\nDZ7+QqNMsnbMAx7wgCxyr321gEPbzUc0rAB9aOy5n2PgEBp3H8uScpvJB1IMq0l7pGfyqgYw3/K4\nqJgUlqHxzTvu8zwJ+P9sVnG3SwqB3YgAM65o2aEwKzIdMl8yHRP5bpkD+SclO/BZWj4mRW3wITJ1\nxuCXPlxmR35DJr8InsklIzHYp4lSNGuQdyaVZ1K2L1OziGHmacUEguTStBykkOZIfWgm52ZutW2S\n8FM3M63vtdVk/Nj2ebh/23el12bCHD+G2XVWMmzb9UwrTOOTRHuwHJeGqe1Mso5335qvOhgjzclM\n6MO0ip4FplbPiGehXbv6v0zAQd75HFiGY2mZqGt+Vz5kUdhcAKpXeRZa3/j2mcL5utUFZvrm72Wq\nFqHtPmpf9Dbh33VefWSG5nZgDhf5rUY0k7h7xfTtWRWjwJQ+S9HXcV+06xGh7ruSTSCw46YrG+xw\nacAbBG4XHBbLeVJLjQFxdDURsJIaKxM0jSf8s6mlRGDNaJ/hGyZIZsX4qWXNWXWxaTU0qmay1IZ6\n2rQT+/melu17GjNTtf1pV+oGN3Np0468Ns3T8dP8tWMn7du06UnfbWSbc+n/Wseu1qe1jp30fdPg\n1/ud/fVXtLNX7TA5cwsM2/KdZ6DdD1qoe+bPfjTmdl/aK9Oy61zrWrXBreA4lhjnpk1HYFRGJTNp\nc3m0/mjP+Zmy1STmJnnhC1+YLgyR7ywrQdD5aEbAVR8VooaP6Za9N376rTBpx4Sgj8ClrC28ZSfc\nxobnqQGXCXobb3Sdan4IMBEa5GLdbv+whz0s/bIRvJL+OQOiZR5MbZMkgrHSjGmQRrAGVOZK7bWB\n3Xvfe7Xcx6tBl6k7AmTyM18gUysiR8YIAVkzdfMJMn03X6x2teEvgr9G79s2BeTHTbGNQOwzPH6/\nWP7Ujmuv+qYP7fM0r4hsmv2m3ce1TrvvavsNr9V+49eF1EyA7DdcvvXQhz40zw+38Ta04940guVe\nWMtM3r43oDseWbq3zLft2bA91kn3sfY2HzXxCLbxDSNibhAujrDYZByCZ9P3CC+C1voI8kv/dGjG\nWcDehGI7xHKxm93sZnk9EWyWfZuFf3k7+r7WOYqA10JoBt+XBjwDEHd4E7Fcp48EDn2Yl3v+tGkF\nYfuRGqTDtJiDo0Aqfl9k3AZvvj7ainW9Bm8EE6U9U9s1gBpYDfZhQsygLgOr9hAbAm4atu1N+/K+\n/bXz+MwnPRzUnQtZ+LNfLCvJCQANqmltzt1IglbX3jciNCEY95dqy7lanyZpo8N+Dd+3fruWSce1\n74ev0+zXrtW+tMTxc7onwzaRr+A427yyDLR9Dj/88LRINCwRLfJzT4ZYDNtr7+HqOG3BE/FHJq4k\np4a5fd0T66ed9/a3v33e/0jmkmu3IylJPlv2O/roo3MSFsuUkmQ9d7RhwWARcZxacLgxes+x2IOI\ngM6J5LTPce03GYF5EvCJ4wE8PG7+rpdWtP3ggw/e9ddaFzgZgdAYc73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EmmuPJ7UF9yH2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cozvFfXIyAQM8SFCDFwpUclnzsRNrsG3MpgK4K137DKbbcW9tPWCeul1q95abKGFV0q/+IHnftm\nh+u5syoSg19vuwInBKE663nTsZ8x1G3p2jAGmEmaLW2fMcD2MaDlelNIDDPdiQbB5n5cDiysBduT\n6F1rurYi2L4hz40E62LqyesQZxgceMQgmWvOymgNjtMG69BBdgcl6Z7yWo9TBltQQk2da9D2lipP\nEGR6TPI8yDY9GrkOy/h0wiBP+4SV235PLhttN2lr1Nb4bHWCfRBq5mNt0dqgtonBN++FD+bJOrK1\na3mIF4ST8dzzPSYBWY6QaLI95C9t+5bVubWN96Qhvk9/4gXh5r7akL5yW5jPIJxcE237ae3bbvG9\n094ffrb0bQHiqlIaw+fDa+X2Pcgp11CDvCZxDxw4kNcws07JE5ltKhfGFp6Y+KSLSntnbS2Ds3Tk\n3dKEoTaLCVa2LzsBOAdh5/eYIPRB7mk/wJmJrUY8psHNvtMgyozHiUoQZh+q6exLvGAFaee2IHme\nffbZk3XZ1pHkGRPW3OttPdfWGvmG4VSu47YtQPqpNKz1qqN+xfMWj3KzQvudcepiO1xMSmZF2/A9\nZeLABsYtwEkfqvD/ERhzDXghtiFFB93xwJKRFSxV0n4I1rGsc5JsSbiO2GsSAxWf9SYqvfZHYjBD\nXyuY1UuLdSdpxN/QenT47mNii451ONItSdBMPgbGYZS8VkZraLQJ1pQF0p01Oyr+GORT4s0HW/xH\n4gifsimNszaVNlU3qYsUPqtcw6yoB0k6VLwkQccIktJIn0FquexAnc2ClORKciHpcvRPTR+kMEwu\nJVNqP+nAjzRFoqNBoZFwaIJykfxIXuKQ8kj9+imVu/flSXrWb603xnCR0ppn+jHsaI9IWtKVhnyk\nRzIUnyRmeYD0p5ykerhQr/tUT+pQGpDY65prlZYiwqAopUjp+CMlwqJ9V5cg66w3jYV2JlHDhQRr\njZ42gUbFkkbsJ0+pUftYj7d+S+olzdpypgw0ETQNqwVLDqRQkn+QaNYhyDr7kf6uD+oHyrhW8L51\nWlbGVNDWZ5VHe9OWwFo9pBkON1IzMCs9+FJ1w0abtUAFbcnj2LCD0H7KyqJ6o4HEq0/qI34r2w00\nFbQbNAPKrL4supW7Qpc7JywD6K+7HYqAdxvxTeZnnRExDtfBJGENDGkY0Ki1GtH69N1guV5AAMiW\nOpmxCDVoU5sO3zVQIx/qZGRrHXyjAwP1JtVuSJtJjMiRGhB5LHIwAPtjnLWdgcqkCM4Gc0QlIEiY\nGAhhKyBIAyV1+mNicrOVIA1kLU3tqOzD5YPpNNvSwUbbcvp936msET+jprVwQij6MoLdSN+clde8\n7ylTw2ne/VH7ak/tblI0dqD2NrnURiboFb6CwJj7gIuAv9IOo18ZEEiypNom2bKgtC41vQ4kLqnH\nuu16Ep6KGWikiWybdOv9WQFpkm5JS9ZuEea0lOc9AwziJt1eG+uyrCtJIMNAqkQIGynj8L26LgQK\ngUJgNxAYk4DXF5N2A4HKI9V0sT6UKiJwNBUeYzDqwelgZu1vtYBckW2TbpHvLOmW6o/UTF2GbP2t\npQakMqRORLpUeFRaDF2QNXX0dPCsQiFQCBQChcDBCBQBH4zJXO8gKNaMzRIZEbKqtaVmqFZGfCwp\nrWMhxLVIcLqA1EvIENkiRlsyZpGt96wJDi2TN6qubnnaOoGAqaJJu1TKLMWt/1UoBAqBQqAQ2DgC\nRcAbx2pTMa3zhfVh7q1l2CEgKQSLbNvaX0uUxMtgZSNB2kPpFrlbh5sO8kPm1l+bdGvdcbXAwMi2\nIiTuz0TB/tjh2h4fs7YQLco63mp1qfuFQCFQCCw6AkXAW2whZMVoiUTLAw+rUZv3WyD5MpDicBwJ\n+mMNOySzFnetTxab9u8iXGu39t62/bLT7yFXqmBGFtZwY5vHupIp4ubhx35Ze2EZfCFuUi0vOrPK\nW+Q7jfze/W6NnjEWC/n1rIf3bi2r5IXAYiJQBLyJduF04S/+4i8mpGv7i0BdzIx9SMC2JVAFbzYY\nDDkrYJ1se4YtIbM2zSNJLhyH0i0perMBmTvxiWROAqdSRuJ7Ze1WG9iKYxuMSZGtG6zD15ok8FbF\nAQcHCRwiuN6Myh/GJkS28LAg5kBhOsQ+6nSQwfKUAZqtKLa0zDJmG76rbJwvsC5WJs5IbKmyncVS\nhq1blhtY7drGgzhZIHM0EfuQs+/Ig6W6bScM5RCr7TJO3mG8x9JauvrWueeem3Wg8XDPARXCu971\nrtzyw5qXIwfO/NuSiUkhb1HcllrqYAiov8ifTUEL4tki5TdjYhd709PJBY9QJnuCrR8mqiaPsd/2\nIC9gLa3hpwmv+kqDpTqHJsruN7jZwMjRtjKTW5NRluMctHDCsd3AAt5vSx76gGsGlXslwFkbazt9\nPHye75Wi751yhqS2FGGrjjiG4NisH4NXbpA/55xz0vECRxVbDTFA9SFF987cDUk5HbZHz8mN+9Of\nMRjn5nmOCWLw74OU1802Bsc8PIEj+TDkSmcInGwsQrjmmmvyEPNYR+6DCGcWKcgrDznnwED8WeH0\n009P5xTwiLXwjO+w9NVCDNiJrwMZQpWfTkY4h+AUJAh8tdcy7VDHZ3s5kMMZxZwrxMCU7SLvFtzn\ncCEIMh1xcNgQE4JePjGYtWgHfQY5pqMMDkD0hyCzLCunDByBcHwRA3kfxm6Tg+hjaSHPSo4ljT72\nJecz74eBXubJKUhsg0mnEUGE6dhf+ZyvrI/Fft50isKhhj6mrLFdKt8JUur1UY4pHI4BryDsPDhB\nOYKQ83AL+XHs4C88eeXB8hxKKCdnG+rlXU5RgmwTlwvD2Ubr4w78CLuEzF9bNwcZBwEUN6TT3tOX\nPxGHfcQkNB1oxIT3oFfE4ZAlyLl/y1vesuK586fhqh7O+3X2uHYN71V9eF1LJyOxzzvrHpOig5xx\nrEhs6kuQeToF4fSCUw8OfeTlvOC9EEIASCcn4Vkuz/iG+aKMHfPGb0xHHKxYlyLMg4C3C1RIIz0v\nUQYZg4ZBsw0mw8+QYNLrlEGMF6qNkrzBMiSofMfAx/uQdENaygFXek58GSPE/tQ+tirlhIAnqZCy\n+zBE68PdZZYxtAu9Q85DA5DF4xELRryQIV8ENvTmI1KsUffhRvOgAZvnn7DWnlnN8FedgyxcY/kg\nvS+Jj8gQXkiaK97j8cjAzUsTj0cmMvBERL6HlXo+a4O7gRe5IRResBCXU2i0BSJc60D0WKZIcuPd\ny2CH1HnT0oYhIWa+rpWztS3y49WJN6rQiqSnp9hGNml3HtFiGSHxQ6jqHdsu8n2TB9fh7nNC6LF8\nkZjKB3mbaJrwmXS0k6zk4znCD4kxJwUhZaf3Mffj2M48hUcZ4WMiGEsn6c0KdiGtZpnjTOneBMrv\nILbf9U7QCmm/10YmQxdffHHPS1X47s54TtwKbUV6P5NGC+rFu5pJSwshwSdmfku8ovE8FUsq+X6L\ng2i1ozK0wEuWyQHvYiYQTv/iYS2MD3MyERqBFnXNT/3B6UjDYALEq9dqwcQD4ZkgreexbrU05nE/\n9mvnRMzkpgW/X565eBbbb2FMAi4VdIwYOxGik6ZfX6rKpk6mVpwVqDFt4bFuy1iK0wuq0fWCPKwP\nUx/6syeXwZctRVSZ1p+plH2nWhsrUGXZa0dlrrxBqB2fzTEAp2qOipNhlzVrqi7qWx6P/DWfv1Sh\nvE5Rx/LFK1AZ2rNMHTsM0rO2OR1iYM1lAScr8RNMbS096VDbUmNSbToQQqC+lae1fmWj2qaipfJl\njMablPX2kMpSDa4Ng7DSeE1bU4nH0XS5TEC9GgNregXjhWk68LvNBzUVpbV3OMCM6pk6XX/Q3lS9\nVLZBvFk+eTCco+Kk8nVwgHgCbHgf448Y5razsUNogSU+Q8GQ/lNFTQ3McQd7AMsQMQBnv6K6liZc\nYW+pxaHzVNLKx4MVNbP4+jDDPSpr+8KVl4paOalkpcOK3tIHv8e8hVFbs8b3nLrTM5629FuHcthS\nJw9xORuheoeVwFsYRxdU4dTRAnWytqF652vc7gL1oZbnFUx/cTiBssDRck4LbDXsKtDm2oTaVbtT\nyduC55AF1/BeK+iv0ypbyyPNIHPWu9Te+pN+xMc0DHkbm+7fs96d5z3tYAxSlhZsedSOnMo0hzLt\nWX1uA4HohEsRdloCpmYLF3QpMZjFx8CTUkI0zYpPqjsSUqyh5bm01KybDdStVGqkj5Y+X7dm+HxB\nL1Ig9SsjKUWIiUKqLd2j0g33i+kbl2qSdGk2SnKK9eyDqkGVTkpugYRINch/cAtBDKnmNIsfBqp+\nbULSJjVbSvBHglQW/ph9knRbCFJIiSwGzvQ3TDqnpiWNS8t9ambvKb/POHAg21cckmd4LEu1o2dU\nu0FeKcnzHU3iJeGSNKmXpU1iky/pukm5JE7lkgZfxvIOQk4phURJwvPMn3SahKqvwZFEKl1lJIWJ\n5z3PSZ+uPXdfv2xqaKpbPphpIjwLcs5P6ZCyYedauVsaNDAkSpJ2q0+TwMWRDlUsaUrdqcpJ9zQN\n+jDVvfyp3Un20qHaFo9moGmN4MxHc5BWqnppfJpU7H0Ssd9IW3KIteY+DhlJdTS1O7/dVN/aQf2U\n2/KA9pS3to2JQKqmwyAxpeAmGct3vQBnfZv03wJp25LLrBAknyrf4TMSvfrvdojJa/qSH2rLjDm0\nLDHJ2u3i7Hh+Y0rAZoFLEeZJwFRFyMNgblAwMLXBxQAz/KOaM2iGr9k+JNRe595MQNDUmsNADRbS\nQZIP5/kGikUNIU3lWm8rnzXCRlLuUdVSucGPal6gioQbdWML1OthKJbO7ts9n9TQiMqgaWCkOhyq\n7A0cBk5redYgqZgRmDIgKvlYA0QW2tE9eVGDuqbCFV+bInefyooQf/VXf3Vy8IL3qYaRiYMEqJvF\nRXJIsX23DkztKw0qXWpYcRCq+re+0+L7royhCZioo8Vv8XzKt/U/pD58FzZNJW3CQZXaiBSZSQvZ\ntPSQZSPjlnZIcjlZoU4ObU2+0+IPP6WL1BCgwzyU23PfEaDrNjkILcTk2u/DxITK3tq8eCYNYayV\nEyDtg0zVs61Zw8skRx4mNnHe7WQpAolS4ZvEOLDD4QfIHPEj8jBiywMKkB7c3JcnlTqyNakz2dNf\nlImNgt+gCS9VunRDwzHshpNrqmf10a9NtJGW36g2t76sb80K+pt1+GEwWbUuPUawVAYTh9BYggiJ\nuA9NyBhF2fE8xyTgckUZvWwjgWqMBSr1HCvlWaqkGMxSRUd1RpXsj7psM4FlLdVg/Pjyj6Wuw7Op\nRvdKCCk1XVPGYJ5H0FHDx/rdpPjUi1SWVIUx8KQKl8cvalZO4vm5joE1rUbbEYRU1NSDnOZPBypk\nqkaqQ9unqEoFKlnqZqpvKkpW7A4CoE5j9U1dzOqc1SsH+o4eVAbPXAehpGWu9qAKlb40Y0RIFST1\nJZUu1ScXolR2Qcrp55nKk1pVfGp0qjvvswRmvfuY8PccxJ75cf5PtSkd7ymLwMJbCJLIPPPL//1T\nzphcDG9lPHGVyxF8LQShZjnkyRELFbIDEtSDOpEaWXqz1PZBmKm61f9ZYfPn7L0WN0g8rbVj0jMp\np7Tgre7qGBJxqo/9PuAqDe95rkyWJRxs4ZAJjl6o/tVN/f218vuUNlzbwR4hgafq2kES6kZ9Tc0s\nHvWttoRtEHIuw7DqpebXbkHq6ZTG78t7VP92EsTkLHGhslYO8S0zxOQif4esuC0jBME2iPPTEgYc\nWNVTqxsv9Evq85gUZf0sJ0wHKnZpx0Qonduop2B7oPZUtzGCdgnBJZcF/G7UYz8GSz36whiHMfgx\nLUXYigRM0o1Bp2ddyZAmOt+KP5IGFR3VF4OijRpozAKccY7ZcsuDWtKMmYU0A4idCNRuZvoMbKjk\n5hFi0EkVL2kfbuoDIxKRQJJoakNGYa5JHuIxtqKiCyJLy1sGKyQXalHqOGpGacX6baY16x/jFZbi\nJBGSNAlToF5kbEWSNJuHqzxJSzFRSgm0qaFj8J5IlFS44pGcfPprUpxrEjIpkyqWpExKI9nG+nVK\ndeJQRZKQScwkYJInaZRVPamRhBqD7iT9JjmSRluew09SWysDtT1p3r0WZ3hNwlU2+emv1LxN7S4+\n6ba9N/z0XiuT9+THKKkZhbUywG/4nmsqaJoA17COtd7EpGkS3FcebSEPEq74JFp/NB3uTafbvquD\na1oPGFGVw50krz/pI55LE/by8HvyWxb0I7gPAytoRmk0JSQi71s+oOlQH8tKMVHLPgoPRmLTQZok\nccZX+rJAmg5HOdNRJ9+DoNOCW/7KCF/W2QzQlGGzGrNJwnWxYQTGlICLgAfNZL0opJMc4P2IqJIM\n/EgKgfjh+lFSaYZh0eDNjV/GbLcPKfegF+RBxYeIw9DkoOfzvsGakZpMXaiJEc121V0GuJBoVgxO\nVPUsgZ8e62xhEJbrXMjJn0EYwSIlAykCRMpUbwaftj3JGqAJEGtUKmSDWrM6HuKCqJEsVTGVHqKj\nbmwBCWvDppKlTpUPIjTIuqZy9GmQR6TIUDoGXfcNsgZK1wZlROXawNuIE3kgKKRNZWoApnIN6Tbj\nIkz1Ndj6RDrSaITn2h9y9ymtth7c8kM4nlG/UrG25+5JrxG07y1d6mcE5Z4/67DyR9Dtnk/5qS/V\nccvP2iwrZM/lJU4j70bC8qV2ha+4JjLiI+FhHq6VX/qew4l609q8iQpchvWRlz/tIL4/camEkXWb\nFMDfb8hzGOtzCJUqWz21EVU2lTOL/GHQv6Qp+P3BSTxtJz3LAyaKJmtxMMrw1bwOg74sD5WtLTze\n0Uepnm1BmhX0ZfHa1iRbrCwhWNN3vrDnFXYegSLgnce4nyUBMyiwXcG2mOfHVgwDnlm1H44fkQF/\nu4Hhjn2UobKaHMBu4Bk7kAxI7S2EOjAHJ9suthoYWpGmpwPymRVMRORnnRt5h5orpRCDvXVUwfYU\n94eB9IH8hoHEYfAfBoRnYB0G7WDtD8kb6JAviQlJGHBJaSYmSMQEAQEZuJGLAV2ZETeCIqkjBQSC\nOKzL02KQSr1r7betY8vXd/HUycDrT7oIUj7q2e6JJ91G6girkSEykpZ3h6TUnltPtZZJC+G5+yZZ\n2oY0alKgnu63yUjLF1GZhHiGYJGca+Tjz3eSq/gmGoiyTSx8F5AX7RF8lLGRr2taHdoWBIls1M9v\nTppwN+mFR5OW5W0tVt7KJl/pwcCkWJ8Tx4QD9gIyNDHRDi0gM3ggVJMDf8NgwmUyKITqNX+vNCmM\nGmm2pKmP6KvTgZRqEmKy3raZsT2Ai7Ix0JwVaGtoaaaDflRh9xAoAt4FrBEwCY/Ex1GDHzpDD+pj\nA4JZLRKaVyB5GVQMFAYNA6aBntUlqXDsQBI0SAwDqdS+3K0GJEpaHVogu0dK2WogPZAipoP2GwYD\nnz3Dw2AShSwNdIiTIRxyapap2sKgafCkvjRYIif9gjSCbLSdgR9RkOQNxtqStI3EkZW8qSqbsRy1\novIhPO/TpiAQEy8kzxo31p9TkkY2yJrqXlA+7yCgRkLiIBiqY1g26Vc8BIvo1ENfMzFA8NoWWfiu\n/FTugmUHUpw6UCkjROm1fto+vSd9Gg2fnElQkyI8UqQ0lUt8xCqeNE021dWEAyFaAkCG6m7fbWzx\nynLAzDukZBoLmiGkbEKgHWhLWll8d78RubbSHvZxawdtLP2hWlnaCHNWMLGWvrLYb+5THZuFL02J\nvccmebFmnEn4bQwJfZiuspvomWybNNG+0Eoo83SfHL5nQiDuMLAGX63cw3h1PT8ExiTgtTezRa/c\nT4EBCGOSkP7S2IPBR3M7FzPgdff2zcIiBuQ0tIjucNDjGFjTqMI+YAelBxGkQYW9lGOHIJcs97Ac\nIVFs2iXj8P0YcHO/bJBCutFU37AS70KjMIy2qesYzPMsZPsyW2DAxdhlGGLgSxeNw3sMhRg9Mbxh\nxMUIKiY/EzeVjFtisEvjrpgspXFWDJr5GZO1NP4JYs39rox6gmjymXSDALqwsM29vTGpS5eQ9qgK\njH9CWs49x3x32w8bxNkx3mF4ZD8wYy0GUEFiadDHIC0mCekeUxoMpcSVj88gvOxD9mgGMWT6DIYY\nNHlun28QVhotwcp1qOrTiEjZYz0995UG2SV20gviSneV6qXe0mv9mJGhdnQgR0wm0hAwiD4Nixgs\nhbo2jZ9CHZ97dhnHhQSc+4rVgyEZg7ogyHTDKd3YhpMYKIv7DLWCXHM/dqiROwZ3MUHIOsAtJh2g\nyDLJUz2FmNSlwVJMJNKYjBEeV5uMt9Tdvt8g0zyxK1+Y+heTi8xTXtxQxkQl95xrE0ZX8rUXl/Gd\nMSImN+nvXT+aFaTnPYZvIWlne8eEIMsbUvCsV/KePBje6Q/6pjEipP00Qlz1pXqwrxAoK+hNNqcB\nD6GG9JN/zfqWpS+ryb0SYjtQkgIrR9aXBi0Dbhg4bbsKQyvokPbSqnQ7ifJ9jCAN4CZQsOYsw+Df\ngvucSoQaM/34qh/rVg4/hvFa/FmfBnaDOrIwsUIKiNOBGyypTaj453YtXkjKmXasJ+bEQ98wqJo0\nGNxDxZ24yosTB4SIPN/0pjeltbY+hFRC0s16qYOJhCAtcQ3unHI4+lE8z31HFtIPrUpadrN8Npib\ncCB1pIpI+ING7oiBRTjSM9hzggEbBGOCwFEGAvXM+yHJdtqORToLWBa+HGFoi5B00xmISRCLZGQu\nD2QTkmDikpX4v3/IXBowYWnKSQnCClV1WkirB/JXP/mbtCFj+Zk8eF+ZhJCS02c5i/ZQf3csyE3w\nQouVvz8TF+SNsO0gkO5GAzLWr0wkTU7UWTvA0eRjrcAZivqb4Pgdmdzx/c2Ry1rB5IEFrvZRH9f+\nKuweAmNaQRcBb6KdDVRm9n40BjhbXniaCrVlfm4iqYWIamuFQcfATaLxwyc5LWIweJv4GOxhjgSm\nAzKzdYPnLcRlcKbZ2G6wFYaHKTghHCQwHUg/yoc4QlWaRIzAhoGUFuvJeSACyRa56UMGfd6oSNZI\nP9YAc+uMATnWgrOvydugHmuYKSnZAhPq4y7Wy4dZ5HYnk6lYs8x3TQpDFZ7SocliqJuTDJVR0AfE\n9wxuJhdhPZzSq89ZgWbD1hkSv8mKtiDdr0V28kG4SNY76q78AjJGoMhOeZuGyCRKG5JskaD+SUL0\n29Mm58Q2Mtu/4IT0lItETfo0WdvtbSUkadu7jA8mHCZpFRYfgSLgXWij8CiTAxf111aDH78fOwKg\nmpxFAltNu94rBAqBQqAQ2H0ExiTgg3eF737990yOVIcVCoFCoBAoBAqBeSCwVEZY8wCs0igECoFC\noBAoBOaBQBHwPFCsNAqBQqAQKAQKgU0iUAS8ScAqeiFQCBQChUAhMA8Eag14HihWGoXAAAF7je3p\ntJ3FXt9hYA1sWw0LYxbBggMhbENhAW37y3rBViLbmlgDs/hdVMv19epRzwuBZUegCHjZe0DVfwUC\nTtkJr0dJkk5fetGLXrQpguN8wr5he6s5WLgwnHTYfiOE28E8qceeXXth47CK3DZkTytHGL7bPtO2\n56wo2P99sd3JyTms8W3PkY69yW1b0ax3OC6xL5bzFQfVzytwCuKULturTCzgFZ6vJnt2t5uPPcHw\nsK/XFi3p2zLV9gRvN/16vxAYG4Ei4LFbYEny52TC3lFbtxDQIgYkdUo4y0AqpFdEhxTtLyVl2ieL\ndOx35WnJPUe22a9q37H74dI0j1EMV4S5X5hzkDe84Q1JgOF/uAuf4+nkgzMRxEzyJQHDhLMN+2A5\n/Ji1h5TkG24zM337bgUepXj5Qkyzgv229kfbWxwHHqTTCk42tkti0rRn2BF+Jiz25fIepo4cUKwV\nvGtSgFQ5WIH1rMDRSfhRTi2C/hNnBadnLp97JdjfzHkJbYdtjGtNlPZKnaqc80Og1oDnh2WltAoC\nBiDnr3L2gaQ4KeCMYdFC+GzO84a5XuRsg3vH8C+cJIxQuS09//zz0yuST04w4iCB9DDFA5MBlgtK\nhMILk3NoOQbhUcmfNLlpRLY8K3GuwVmEeOEjOs8cRjoItbknHGKE6BF6I1/PwqdyumYkDQ8DhzE8\nM/F0xpkHJxbOsuYVjMvR7QZSfvhGTicf0uIAA0bcN64VTCJ4uopDUPJMX45SXE8HOHG+wquaiYqy\nU+1LX532QnAOsrOJTapI80iYa88KhUBDoAi4IVGfO4IAYiDlxMk6OaD6zpsTV4jzDtSxXP/x9c29\nIUmP1BonLqWkuV5+JDOuJ4eBr2iDKOkdcfFY5aB1rhd5bKJWJpGRBE0sDLrKQBJUzzhpK522kJZJ\nzdxLWudFMDw/wQPJ8FxFfc09pHVjkxbru6TEFniDQnTTwZqy9eAW+Cwm7SL58847L6WuOBwhH5OI\neY/abkCkvHkNA6maF6i1Aoldf4AhSZn6GkY0B8MAG4E70ThiMK/hZsLC29QiB9oNkxN9xdICxz1x\nvGD6CDchq1AINAQO/jW3J/VZCMwBgTiFJ90tGowELgMRE7XuPAOjJ9IUFS8SQ7okSdIW/7z8M8+S\ntIZlILmK2wIpPY4TTPIl/TJ8MnFAsnw+k46RCDWytVl+i6liSTzyQkYkYe4fm/tSUjIVN0KUPvWz\nNU5rs9StiJfzf2rrpt5t5TGpIEkNVbBIm1RLBd4Cl5XSjpN+8hAGEiPSol6X/kY9uME0zo2eHILQ\n0veJROFx5ZVXTm5TRZskrBVMkk499dRJFMZoXHby+zwM1tBhNjx0g89nfWcRtSet7B/84AdTK8BT\nnsmDyZQ+Y3IXp0HlUkSLW5+FwFemzYXFwiJgwIkzbJMcHBJgwCWV8Yu86MEgOi0pUcWRoOYZEAF1\nrIMKBGu3CNIAT+qwnku1/JjHPOYgKbeVA3FRJSNNki/jKIcZIEn1gDe/xYK1PASkbagVEQ+pjVSM\nXKmbpaU8iIPRlHSVSdoOYjAZcXgCCcl7niFy6mqSOMmPr+4WSJgmAg5gcOKSMlDtX3zxxS1KStak\nfmuP1NkOWCBlkxxh4j1EThL3t1pgTMV9q7VX5UYsQ1/Pym6SYNJiogAfE5DVTgxq+ZgowHM4CYDj\ndFlgTTKGDelePai9YdIORkBq/Gg7CEGf0sa0BmMG6+C0DiR6Wg2TEssUfImrw3bX3sesW+U9fwRK\nAp4/pnNP0YBs8EEycYZonvjjR73IkkADAQmQRknCLbhnXXKeYZroERwibCpckghp1f3VgjKRQk0Y\nHGtHcmHc5BAOxIdsEAgJ2BqteNJFhIjAaUoIP85aTqmY4RN1L2lOPCSLMJGLOAgbcSN6xIKYqJOp\np61HM1QaTl5IsUiGtGw9GGkx3BpKnQZ6qnBSssmGdVNkbk0YCVtrto7q+EAHMMwK1OfiS5dGwdo9\n4y/S8DAgZEZpJFr90QSItL9WEDfOwJ1I1jQMcWZuTo6m34OfZ7ClqkZgiLYZeVnX1p7ahtrfRIA2\nYcxgqcEEgbRr4qIt9A9tSfOhvhUKgQkCMYgvRQg1XB++nPdkXWP7xeSw91aBGGz6kEra14X+DGmM\nxVUfJwnlIe1PfepT+yCfuZY5TubJg8wdji7EoRt9GDetaPMwnOqDOLeUb0gyeeh7rC/3D3/4w/tY\n0+61SxBrH+rYPIj9wgsvzEPjY4LRx2DbB2nlIfGXX355HyrJLFOoW/sg9HwnyChxCTV5H8SVh9y7\nDgmqDyLPZ2GoleWNk5byexBefnc/TkTqr7322hX1Cam0D4m7D/LMMqqz8obFcsZzqDyMlCEk9ExD\n+YYhjLf6IJKM1+4HkfQxkchD5mMtto8TwPrYetQeb+ozJPE+rLz7MFjrg7j7mPSs+X5Yp/dhhNXH\nhGESL7ZeJaaTG3ERKvf+pJNOGt7a9etY6+1jAjPJN9a6s11f8IIX9HFa0uR+XSwOAi972cv6OCt+\nlAKRopYi7GUCDpXjQW2k08Rs/6D7i3ojpIE+zhruY421D9XhjhQz1J99SKhJfiE9JWG2wT2MppLA\nQl285byRX0iBORnygzWpCJVxpockQuLs47jBJLtwqtHHMYB9m3xorzDY6kMN3of1dB+q4HwPQYZk\n3MdZvTkpCcm0D/VuH6rpjNsKG+f/Jgm17z5DG9KHynN4K0koVMxJVnHUYS9f388+++zeb8DkJ1S6\nfVgs9yZxyo+MY816ko6JRWhdJt9DDd2H5JmkbHIQ2oE+JOlMN6T1SbzdvIBrSJMHZRlagYPu7eYN\n/S00KX1oKvrQbPQmPLF8tJtFqLw2iUAR8CYB20r0vUzAYbjTx3rYpNpm/wb/Jg1NHtRFH1tXcmIS\n+3P7WMNMCRS5Ib1Q284NoTDwSgIcJhiGZT0JiPQZB9P3oXbsxYt1ySS5OPR+GH1yTbqMvb99qHDz\nPWRJwo3140mcMOjpY01x8t0FqfBVr3rVinu+hIo5JWhl0E/CKCwl9Ub8SDtU232oqfPdMIzqY3vT\nJB1SOOm9BZMC6ZCkWzChQvChKm+3dvVTW8b2pD5sIib5wmOI2eTBLl/Eckh/6aWX9iZXe0VLtcsQ\nLVR2YxJwGWHFyLLogaWr9UMHfjPAcvA7C9eh5eui12G3ymcN1p9gvdVe3Z0IDICmtwT5HiSba8TW\nXRkH2YZiPdnap/VlxkvTwXqyrVPWhq2lBrGlB6ihQREDMuvCocbP+llfDDVw98///M/TyaXhkv5h\nzdY2KZ+2OsmHURXLYtuBgqDzXf3InuQWGBEx1GIUxgjKGr69y7yCtWA9Vn2tWY8RWLXbH6zs1okZ\nwtl21qztxyhTy1M7snOoUAish0AR8HoILcBzg51BE/GyHn7JS16ywjhnAYq4dEVgiYxUP/CBD3QP\netCDkgBYTHPewRjJFpRGtsgBiWnHWYGRFsMn7yNMRkchIqQFbYvP61Sot9O5Bi9ZtggxlGJtPSvI\nq+WHSGO9NbdkMVJiCGQ/cAusmaXfAkMqVryMnBj/mfQxtgq1e4uSlt22X5nkjBXgj4j9LhhnhZYr\n3W2OVZ7KtxDYLAJFwJtFbKT4LFINohUWAwH7PO0zRlxtf+c73/nO3HZE4mT5SgI2YaLBIFW6t1og\nzZpkkZaPOeaYifOOYXxWz56TpJH+WukN32vXrKL9IVQW3bbMsLi2JYjjjmHQ30iWLZCgOZcg0ZPu\nWSWHSjql/RZnjE9W3f4qFAJ7EYFDKOP3YsE3W2Z7GkkNYR272VcrfiGwKgIOIbB9yElGwy1Dtp2Q\nhpEk9XEYP62axhgPqLCpr0nJHIdsJPCVTTo3AfAOBxq1r3UjyFWcRUbgjDPOSG2PbXq7HUoC3m3E\nK799hYC9w7P2NNv/6W9RAych/jYTSL/nnHPOZl6puIVAIbAGAuWIYw1w6lEhUAgUAoVAIbBTCBQB\n7xSylW4hUAgUAoVAIbAGAkXAa4BTjwqBQqAQKAQKgZ1CoAh4p5CtdAuBQqAQKAQKgTUQKAJeA5x6\nVAgUAoVAIVAI7BQCRcA7hWylWwgMELA32BY4e3mdLhS+qQdP53dpV6G9whyEtJOg5pd6pVQIFALz\nRKAIeJ5oVlpLh0D4H05HHIjV2b+8Q00HZzg7uo8jFUcB8tjE49V11103HXVb37mZ5CUtTuDpwhdx\n7vHlvrRCIVAILCYCRcCL2S5VqhEQcHYuf8fOlnUGM3/Pa4Xrr78+z9V1eD1ifcUrXpHvcvgyDAiX\na8rme5kXKt+dAzzPEAcq5NnDnGUok7OB4yCP0fw1z7NulVYhsB8RKALej61addo0AtxAxilAXZyc\n1MVRfd1hhx2WDvW5klwtkDTjlKp06ygOCdgBAW9729tWvBJnH+ch7cObnHeQjOcZ4mjBPOy+pcl1\nZJxbvMKHc3tWn4VAITA+AkXA47dBlWABEDjzzDOTTPlk5i+ZezqfV1555aqlu+OOO/KUoGGEI444\nokO4w8BXcRxNt0ISffOb39wdeeSRKRUjbirsOBZw+Nqmrx1IMD1hII07XKFCIVAILB4CRcCL1yZV\nohEQiDNcu+Hxf4rgoIW1jts7+uiju7POOmtSWnEdQ/cDP/ADk3sunvKUp3QveMELktDPPffcvOZD\n+vWvf30SvYMOXvva13YvfOEL80CGFS9v4suBAwfyxKSmOnfqkQMVHG9YoRAoBBYPgSLgxWuTKtEI\nCDjWbniW7N13352GUtOkPCzaaaedltIun88IFPnGIfdJuMN4rk855ZQ8ktC5zsiY9Ov82nZIA5K0\nXjssw3Qa630//fTT80xhxxWecMIJeaSgc4GdbFShECgEFg+BOoxh8dqkSjQCAg67f+xjH9s58YcE\ni0id9rPWEZBOAkKithQ5Iejkk0/ONFYrPjJvhP72t789LaOHcZ2o9OEPf3h4a1PX97rXvXIisKmX\nKnIhUAiMhkAR8GjQV8aLhIBj+Zxxe8kll6Qa2J5da7MbCVTRmw1I/td+7de6q666qjvkkENy7fbE\nE0/MLUqbTaviFwKFwN5EoAh4b7ZblXoHEDj00EO7U089dQdSPjjJH//xH899wE9+8pO75z3ved3f\n/d3fdb/yK7/SHXfccQdHrjuFQCGwLxEoAt6XzVqV2gsIvO51r8stQpx3sL5+0pOetBeKXWUsBAqB\nOSFQBDwnICuZQmArCLCQrlAIFALLiUBZQS9nu1etC4FCoBAoBEZGoAh45Aao7AuBQqAQKASWE4Ei\n4OVs96p1IVAIFAKFwMgIFAGP3ACVfSFQCBQChcByIlAEvJztXrUuBAqBQqAQGBmBIuCRG6CyLwQK\ngUKgEFhOBIqAl7Pdq9aFQCFQCBQCIyNQBDxyA1T2hUAhUAgUAsuJQBHwcrZ71boQKAQKgUJgZASK\ngEdugMq+ECgECoFCYDkRKAJeznavWhcChUAhUAiMjEAR8MgNUNkXAoVAIVAILCcCRcDL2e5V60Kg\nECgECoGRESgCHrkBKvtCoBAoBAqB5USgjiNcznavWo+IwC233NJdc8013Z133tkdc8wx3Td90zeN\nWJrKuhAoBMZCoCTgsZCvfJcSgU996lPdc57znO7mm2/u7r777u6oo47qrrvuuqXEoipdCCw7AiUB\nL3sPqPrvKgLHHXdcd8EFF3RPe9rTMt9nPOMZ3RlnnJH3HvrQh+5qWSqzQqAQGBeBkoDHxb9yXzIE\nHve4x03IV9VJwO599KMfXTIkqrqFQCFQBFx9oBDYRQRuvfXW7rbbbluR4/ve977uAQ94wIp79aUQ\nKAT2PwJFwPu/jauGC4TAKaec0p166qndjTfe2H3605/uTjjhhO4JT3hC/i1QMasohUAhsAsI1Brw\nLoBcWRQCDYHnPve53QMf+MDurLPO6u65557uR3/0R7uf/umfbo/rsxAoBJYIgSLgJWrsqupiIIB0\n/VUoBAqB5UagVNDL3f5V+0KgECgECoGRECgCHgn4yrYQKAQKgUJguREoAl7u9q/aFwKFQCFQCIyE\nQBHwSMBXtoVAIVAIFALLjUAR8HK3f9W+ECgECoFCYCQEioBHAr6yLQQKgUKgEFhuBIqAl7v9q/aF\nQCFQCBQCIyFQBDwS8JVtIVAIFAKFwHIjcEgfYRkg+Md//Mfu+OOP777zO79zoap7ww03dDfddFN3\n6KGHLlS59nJheJi66667usMOO2wvV2Ohym6YuP3227vDDz98ocq11wvDL3hhOt9WhOmxxx7b3fve\nG/Mz9bGPfax7z3ve0z3iEY+Yb0E2kNrSEPAGsBglyqWXXtp98YtfLHeEc0T/7//+7zu4vu51r5tj\nqsudlD568sknd1dfffVyAzHn2iOKa6+9ds6pLndyBw4c6K644orufve738IDUSrohW+iKmAhUAgU\nAoXAfkSgCHg/tmrVqRAoBAqBQmDhESgCXvgmqgIWAoVAIVAI7EcEioD3Y6tWnQqBQqAQKAQWHoEi\n4IVvoipgIVAIFAKFwH5EoAh4P7Zq1akQKAQKgUJg4RGobUgjN9EXvvCFzh7Lr/marxm5JPsn+y99\n6UsdXB/ykIfsn0qNXBN99L/+67+6r//6rx+5JPsr+09/+tPdkUceub8qNXJtPvOZz3QPe9jDukMO\nOWTkkqyffRHw+hhVjEKgECgECoFCYO4IlAp67pBWgoVAIVAIFAKFwPoIFAGvj1HFKAQKgUKgECgE\n5o5AEfDcIa0EC4FCoBAoBAqB9REoAl4fo4pRCBQChUAhUAjMHYEi4LlDWgkWAoVAIVAIFALrI1AE\nvD5GFaMQKAQKgUKgEJg7AkXAc4e0EiwECoFCoBAoBNZHoAh4fYwqRiFQCBQChUAhMHcEioDnDunW\nE/yZn/mZ7rTTTtt6AvVmInDXXXd1L3/5y7unPvWp+XfmmWd2vGNV2BoCDow/+uiju2/8xm/sTjrp\npO5zn/vc1hKqtyYI/NEf/VH3Qz/0Q92TnvSk7qd+6qe6f/mXf5k8q4vtIXDNNdfsGS94RcDba+u5\nvf2ud72ru+KKK+aW3jIndNFFF3U33nhjd9111+XfRz7yke7iiy9eZki2XPebb765e/azn9298Y1v\n7D760Y8mCZ9xxhlbTq9e7DquEn/hF36hQ8LXX39998xnPrN76UtfWtDMAQGTw1/8xV9M975zSG7H\nkygC3nGI18/glltu6X7913+9e/GLX7x+5IqxLgKkinPPPbe7z33uk3/f9m3f1v3N3/zNuu9VhIMR\n+OAHP9g9/vGP777jO74jsdRHr7zyyoMj1p0NI/DlL3+5u+yyy9JfsZf01/e///0bfr8iro6A/mly\nsxf8QKtFEfDqbblrT37u536uO+ecc7r73//+u5bnfs7ou7/7u7ujjjoqq3jbbbd1b33rW7sTTjhh\nP1d5x+r2qU99asVhAZzcf/7zn+/uvPPOHctzvyf88Ic/vDvmmGMm1fy93/u97vjjj598r4utIXD5\n5Zd3hx12WGoUtpbC7r91793PsnIcIoAc7ne/+3U/8iM/0n3oQx8aPqrrbSJg3fdZz3pWh5BPPvnk\nbaa2nK/Tzhx++OGTyuurwu23397d9773ndyvi60h8Ja3vKW76qqrug984ANbS6DeSgSo9V/1qld1\nf/3Xf9397//+755BpSTgXW4qR+Qdeuih+UcNZe2HMcY73/nONMT45Cc/meuWu1ysPZ3dENN3v/vd\nWRfk+2M/9mPdPffckxLwnq7giIU/4ogjVgxot956a0oZD37wg0cs1f7I+vzzz+/OOuus7s///M+7\nb/iGb9gflRqpFqeffnoaCr7vfe9LPP3+jamLrqkpCXiXO8x73/veJAXZ3ute9+oe+9jHdn6Iwk03\n3dTdcccd3SWXXNJ93/d9X96rf+sjMMQUnnfffXdKvsj37W9/e0521k+lYsxCADF84hOfmDxy/chH\nPnLyvS62hgBDQctOyNcae4XtIUCoYdDmD+kaR3/zN3+z+/7v//6F1tTUecDba/e5vv1bv/Vb3Q03\n3DAh5LkmvkSJ/fZv/3b3B3/wBx1puKlJ/UBrjX3zncBg9qhHPSq1CLYi2SpnDfPVr3715hOrNxKB\nj3/8490Tn/jEzs4Hny3Q5FTYPgLsFp785Cd3n/3sZ7ef2A6nUBLwDgNcye8+AgiYKh9RtHDgwIEc\n8Nr3+twYAiYw5513XnfiiSd2D3zgA7tv/uZv7t7whjds7OWKNRMBW7oYBx577LErnrv31V/91Svu\n1Zf9jUBJwPu7fat2hcBcEKDWt/5ba79zgbMSKQQSgSLg6giFQCFQCBQChcAICJQV9AigV5aFQCFQ\nCBQChUARcPWBQqAQKAQKgUJgBASKgEcAvbIsBAqBQqAQKASKgKsPFAKFQCFQCBQCIyBQBDwC6JVl\nIVAIFAKFQCFQBFx9oBAoBAqBQqAQGAGBIuARQK8sC4FCoBAoBAqBIuDqA4VAIVAIFAKFwAgIFAGP\nAHplWQgUAoVAIVAIFAFXHygECoFCoBAoBEZAoAh4BNAry0KgECgECoFCoAi4+kAhUAgUAoVAITAC\nAkXAI4BeWRYChUAhUAgUAkXA1QcKgUKgECgECoERECgCHgH0yrIQKAQKgUKgECgCrj5QCBQChUAh\nUAiMgEAR8AigV5aFQCFQCBQChUARcPWBQqAQKAQKgUJgBASKgEcAvbIsBNZC4M/+7M+6v/zLv1wr\nykI8W6ucL37xi7tXv/rVC1HOKkQhsKgIFAEvastUuZYWgfPPP7/7z//8z4Wv/14p58IDWQVcWgSK\ngJe26avii4jA7//+73fvec97ule+8pXdH/7hH3a3335797M/+7PdIx7xiO4hD3lI9xM/8RPdrbfe\nmkV/xjOe0b3mNa/pHvawh3Xvfve7u0suuaR71KMe1T30oQ/NeJ/73Ocy3jHHHNN9/OMfn1T36KOP\n7j75yU92d999d/fCF76wA8qPdgAABLJJREFUe9CDHtQ9+tGP7l772tdO4gwvZqU7Xc6+77uXvexl\n3ZFHHtn94A/+YPcf//EfwyTquhAoBGYgUAQ8A5S6VQiMhcBznvOc7thjj+3OPvvsJNHf+Z3f6W68\n8cbuH/7hH7rrrruu+6d/+qfuT/7kT7J4//Zv/5aq6gsuuKB7/OMf373oRS/q/vRP/zTj33bbbd2b\n3/zmSbwvfelLkyp5z/crrriicy19BP4bv/Eb+X0SMS7uuOOOmelOl/ONb3xj91d/9Vfde9/73u70\n00/vrr766mEydV0IFAIzELj3jHt1qxAoBEZC4L73vW93n/vcpzv88MM7189+9rO7U045pfu6r/u6\n7otf/GL3uMc9rvvMZz4zKd1LX/rS7sCBA92dd97ZffnLX05CRo7veMc7ukMPPXQSb9aFfP793/+9\ne//739/98A//cPff//3fmecw7iGHHLJqusNyXnnllVnOb/3Wb+38/e7v/u4wmbouBAqBGQiUBDwD\nlLpVCCwKAl/1VV/VveQlL0k18/HHH9/dcMMN3T333DMp3iMf+ci8RtaXXXZZd9FFF6W6Wtx//dd/\nncSbdXHiiScmwZ966qmZ/stf/vIk8mHcjaZLin7KU54yefVpT3va5LouCoFCYDYCRcCzcam7hcBC\nIGD919rvhz70oe7DH/5w9z3f8z2d9dYWELRA+v2u7/qu7vrrr8+/BzzgAakK9kwcErKAvD/72c/m\ntXtnnHFGd9NNN3Vvfetbu6uuuqq78MIL81n7t1a6LY5Pa88f+chHJrc+9rGPTa7rohAoBGYjUAQ8\nG5e6WwiMhgD18//8z/9k/rfcckvHaIoKmmETA6277rrroLLdfPPN3bd/+7dnnCc84QndcccdN4nD\nSOtv//Zv8/vb3va2yft//Md/3P3kT/5kR80s/rd8y7dM3rn22ms7aa6V7rCcz3zmM1MCt/bMwMt6\ncIVCoBBYG4FaA14bn3paCOw6AqyIf/7nfz5JmFqYdfF5552Xku9JJ52UaujpQiHos846K8kaMX7h\nC1/okK1w5plnds9//vNzXy41MaIWnvvc5+Za8VFHHZWS8ROf+MRUSXv2rGc9q2PpbH15tXSH5fzl\nX/7lNBqzRi187/d+b37Wv0KgEFgdgUNCnfUVfdbq8epJIVAI7CICrI8ZOVEf+4mShI844ogNlYAx\n1dd+7deuiEtqRsoPfvCDV9z3RV6soqmt1wqz0h2W07uf//znu/vf//5Z7rXSqmeFQCHQdUXA1QsK\ngUKgECgECoEREKg14BFArywLgUKgECgECoEi4OoDhUAhUAgUAoXACAgUAY8AemVZCBQChUAhUAgU\nAVcfKAQKgUKgECgERkCgCHgE0CvLQqAQKAQKgUKgCLj6QCFQCBQChUAhMAICRcAjgF5ZFgKFQCFQ\nCBQCRcDVBwqBQqAQKAQKgREQKAIeAfTKshAoBAqBQqAQKAKuPlAIFAKFQCFQCIyAQBHwCKBXloVA\nIVAIFAKFQBFw9YFCoBAoBAqBQmAEBIqARwC9siwECoFCoBAoBIqAqw8UAoVAIVAIFAIjIFAEPALo\nlWUhUAgUAoVAIVAEXH2gECgECoFCoBAYAYH/ByiDAMrRu+45AAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 125
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As a note. We will start to build complex models. Especially once we build\n",
      "them in a MLE framework, it is useful to understand formula objects in **R**.\n",
      "`?formula` provides a useful example of how to do this with `paste()`, and I will\n",
      "use that."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 125
    }
   ],
   "metadata": {}
  }
 ]
}