nikibobi/regression.ipynb

## regression.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regressions\n",
    "Author: _Borislav Kosharov_\n",
    "\n",
    "I am going to show two types of regression using python and scikit learn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First create our data. We have 6 points with their `x` and `y`. `x_col` is a column vector of `x` and is used to feed it into the `model`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0],\n",
       "       [1],\n",
       "       [2],\n",
       "       [3],\n",
       "       [4],\n",
       "       [5]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(6)\n",
    "x_col = x.reshape(-1, 1)\n",
    "y = [1.2, 1.8, 3.2, 3.8, 5.2, 5.8]\n",
    "x_col"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we create our linear regression model and train it on our data `x_col` and `y` using `model.fit()`\n",
    "\n",
    "Then we use `model.predict()` on the same `x_col` as `x`, but new `y` - `y_pred` predicted from our model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = LinearRegression()\n",
    "model.fit(x_col, y)\n",
    "y_pred = model.predict(x_col)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can print the model's coeficents that define the line\n",
    "$$f(x) = Ax + B$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'f(x) = 0.966x + 1.086'"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"f(x) = {:.3f}x + {:.3f}\".format(model.coef_[0], model.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And finally we can plot our original points and the resulting line model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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GtxvO+KvGc8pJpzgdS6TEVO4iIsX2F+xn3JJxTFw+kVZntmJl3EouaXyJ07FE/KZyFxEB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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f037d816e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.plot(x, y_pred, color=\"green\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic Regression\n",
    "_To Be Continued..._"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
	{
	"cells": [
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"# Regressions\n",
	"Author: _Borislav Kosharov_\n",
	"\n",
	"I am going to show two types of regression using python and scikit learn"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"## Linear Regression"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 1,
	"metadata": {
	"collapsed": true
	},
	"outputs": [],
	"source": [
	"from sklearn.linear_model import LinearRegression\n",
	"import matplotlib.pyplot as plt\n",
	"import numpy as np"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"First create our data. We have 6 points with their `x` and `y`. `x_col` is a column vector of `x` and is used to feed it into the `model`."
	]
	},
	{
	"cell_type": "code",
	"execution_count": 2,
	"metadata": {
	"collapsed": false
	},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"array([[0],\n",
	" [1],\n",
	" [2],\n",
	" [3],\n",
	" [4],\n",
	" [5]])"
	]
	},
	"execution_count": 2,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"x = np.arange(6)\n",
	"x_col = x.reshape(-1, 1)\n",
	"y = [1.2, 1.8, 3.2, 3.8, 5.2, 5.8]\n",
	"x_col"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"Then we create our linear regression model and train it on our data `x_col` and `y` using `model.fit()`\n",
	"\n",
	"Then we use `model.predict()` on the same `x_col` as `x`, but new `y` - `y_pred` predicted from our model"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 3,
	"metadata": {
	"collapsed": true
	},
	"outputs": [],
	"source": [
	"model = LinearRegression()\n",
	"model.fit(x_col, y)\n",
	"y_pred = model.predict(x_col)"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"We can print the model's coeficents that define the line\n",
	"$$f(x) = Ax + B$$"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 4,
	"metadata": {
	"collapsed": false
	},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"'f(x) = 0.966x + 1.086'"
	]
	},
	"execution_count": 4,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"\"f(x) = {:.3f}x + {:.3f}\".format(model.coef_[0], model.intercept_)"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"And finally we can plot our original points and the resulting line model"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 5,
	"metadata": {
	"collapsed": false
	},
	"outputs": [
	{
	"data": {
	"image/png": 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RkXKhchdXK7JFvJT5EqPmj6J29dq89z/v0bNlT6djiYiUK5W7uFb2zmwSUhNY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\neTvwzfC4zOk8TjPG7ATutta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	"text/plain": [
	"<matplotlib.figure.Figure at 0x7f037d816e48>"
	]
	},
	"metadata": {},
	"output_type": "display_data"
	}
	],
	"source": [
	"plt.scatter(x, y)\n",
	"plt.plot(x, y_pred, color=\"green\")\n",
	"plt.show()"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"## Logistic Regression\n",
	"_To Be Continued..._"
	]
	}
	],
	"metadata": {
	"anaconda-cloud": {},
	"kernelspec": {
	"display_name": "Python [conda root]",
	"language": "python",
	"name": "conda-root-py"
	},
	"language_info": {
	"codemirror_mode": {
	"name": "ipython",
	"version": 3
	},
	"file_extension": ".py",
	"mimetype": "text/x-python",
	"name": "python",
	"nbconvert_exporter": "python",
	"pygments_lexer": "ipython3",
	"version": "3.5.2"
	}
	},
	"nbformat": 4,
	"nbformat_minor": 1
	}