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Created November 30, 2015 11:28
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Think Stats 2, 12장 연습문제 해답
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"통계적 사고 (2판) 연습문제 ([thinkstats2.com](thinkstats2.com), [think-stat.xwmooc.org](http://think-stat.xwmooc.org))<br>\n",
"Allen Downey / 이광춘(xwMOOC)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from __future__ import print_function\n",
"\n",
"import pandas\n",
"import numpy as np\n",
"import statsmodels.formula.api as smf\n",
"\n",
"import thinkplot\n",
"import thinkstats2\n",
"import regression\n",
"import timeseries\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 연습문제 12.1\n",
"\n",
"이번 장에서 저자가 사용한 선형모형은 선형이라는 명백한 결점이 있고, 가격이 시간에 따라 선형으로 변할 것이라고 예측할 이유는 없다. 11.3 절에서 했던 것처럼, 2차항을 추가해서 모형에 유연성을 더할 수 있다.\n",
"2차 모형을 사용해서 시계열 일별가격을 적합할 수 있고, 모형을 사용해서 예측값도 생성할 수 있다. 2차 모형을 돌리는 RunLinearModel 버젼을 작성해야할 것이다. 하지만, 예측을 생성하는데 timeseries.py에 나온 코드를 재사용할 수도 있다."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Intercept 13.7 (0)\n",
"years -1.12 (5.86e-38)\n",
"years2 0.113 (4.82e-07)\n",
"R^2 0.4553\n",
"Std(ys) 1.096\n",
"Std(res) 0.809\n",
"Writing timeseries11.pdf\n",
"Writing timeseries11.eps\n"
]
},
{
"data": {
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1Zv/BI5SWlPLVkg385b7r7RrDqaw8jhzLAMyjaS0TkmgYAf4+tG/XmtS0U5SW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\nO1+CfjXnvEpy+13GWEOgDijWKOQynF+ThVc/6AEgLMuTBn2D2YaTHZ6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KUpPwh+bT6DAJ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\noE8IIYTECAr6hBBCSIz4/8SD0gDkGzqkAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xacdd36ac>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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yjuNMhNr3fYxGo8x6bt+P8fzzu/C8LrReQ6HQRqGg8NhjZM1zAxe28KPIRxj2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4AAAg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\ngg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xac93a4ac>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<matplotlib.figure.Figure at 0xac8efecc>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def RunQuadraticModel(daily):\n",
" \"\"\"Runs a linear model of prices versus years.\n",
"\n",
" daily: DataFrame of daily prices\n",
"\n",
" returns: model, results\n",
" \"\"\"\n",
" daily['years2'] = daily.years**2\n",
" model = smf.ols('ppg ~ years + years2', data=daily)\n",
" results = model.fit()\n",
" return model, results\n",
"\n",
"def PlotQuadraticModel(daily, name):\n",
" \"\"\"\n",
" \"\"\"\n",
" model, results = RunQuadraticModel(daily)\n",
" regression.SummarizeResults(results)\n",
" timeseries.PlotFittedValues(model, results, label=name)\n",
" thinkplot.Save(root='timeseries11',\n",
" title='fitted values',\n",
" xlabel='years',\n",
" xlim=[-0.1, 3.8],\n",
" ylabel='price per gram ($)')\n",
"\n",
" timeseries.PlotResidualPercentiles(model, results)\n",
" thinkplot.Show(title='residuals',\n",
" xlabel='years',\n",
" ylabel='price per gram ($)')\n",
"\n",
" years = np.linspace(0, 5, 101)\n",
" thinkplot.Scatter(daily.years, daily.ppg, alpha=0.1, label=name)\n",
" timeseries.PlotPredictions(daily, years, func=RunQuadraticModel)\n",
" thinkplot.Show(title='predictions',\n",
" xlabel='years',\n",
" xlim=[years[0]-0.1, years[-1]+0.1],\n",
" ylabel='price per gram ($)')\n",
"\n",
"transactions = timeseries.ReadData()\n",
"\n",
"dailies = timeseries.GroupByQualityAndDay(transactions)\n",
"name = 'high'\n",
"daily = dailies[name]\n",
"\n",
"PlotQuadraticModel(daily, name)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"## 연습문제 12.2\n",
"\n",
"9.2 절에 나온 HypothesisTest을 확장하는 클래스를 정의하는데 명칭은 SerialCorrelationTest이다. 데이터로 시계열과 시차(lag)를 받아서, 주어진 시차를 갖는 시계열 데이터의 계열상관을 계산하고 나서, 관측된 상관에 대한 p-값을 계산한다.\n",
"\n",
"이 클래스를 사용해서 원가격 데이터에 나온 계열 상관이 통계적으로 유의적인지 검정한다. 또한, 선형모형과 (만약 이전 예제를 수행했다면) 2차 모형의 잔차를 검정한다."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.485229376195 0.0\n",
"0.0757047376751 0.004\n",
"0.0560730816129 0.042\n"
]
}
],
"source": [
"class SerialCorrelationTest(thinkstats2.HypothesisTest):\n",
" \"\"\"Tests serial correlations by permutation.\"\"\"\n",
"\n",
" def TestStatistic(self, data):\n",
" \"\"\"Computes the test statistic.\n",
"\n",
" data: tuple of xs and ys\n",
" \"\"\"\n",
" series, lag = data\n",
" test_stat = abs(thinkstats2.SerialCorr(series, lag))\n",
" return test_stat\n",
"\n",
" def RunModel(self):\n",
" \"\"\"Run the model of the null hypothesis.\n",
"\n",
" returns: simulated data\n",
" \"\"\"\n",
" series, lag = self.data\n",
" permutation = series.reindex(np.random.permutation(series.index))\n",
" return permutation, lag\n",
"\n",
" \n",
"def TestSerialCorr(daily):\n",
" \"\"\"Tests serial correlations in daily prices and their residuals.\n",
"\n",
" daily: DataFrame of daily prices\n",
" \"\"\"\n",
" # test the correlation between consecutive prices\n",
" series = daily.ppg\n",
" test = SerialCorrelationTest((series, 1))\n",
" pvalue = test.PValue()\n",
" print(test.actual, pvalue)\n",
"\n",
" # test for serial correlation in residuals of the linear model\n",
" _, results = timeseries.RunLinearModel(daily)\n",
" series = results.resid\n",
" test = SerialCorrelationTest((series, 1))\n",
" pvalue = test.PValue()\n",
" print(test.actual, pvalue)\n",
"\n",
" # test for serial correlation in residuals of the quadratic model\n",
" _, results = RunQuadraticModel(daily)\n",
" series = results.resid\n",
" test = SerialCorrelationTest((series, 1))\n",
" pvalue = test.PValue()\n",
" print(test.actual, pvalue)\n",
"\n",
"TestSerialCorr(daily) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 연습문제 12.3\n",
"\n",
"예측을 만들어 내는데, EWMA 모형을 확장하는 몇가지 방식이 있다. 가장 단순한 방법중의 하나는 다음과 같다:\n",
"시계열 EWMA를 계산하고, 가장 마지막 점을 절편 inter으로 사용한다.\n",
"시계열의 연속 요소사이에 EWMA 차이를 계산하고, 가장 마지막 점을 기울기 slope로 사용한다.\n",
"미래 시점에 값을 예측하는데, inter + slope * dt을 계산한다. 여기서 dt는 예측 시점과 가장 마지막 예측 시점의 차이다.\n",
"이 방법을 사용해서, 마지막 관측점 다음 연도에 대한 예측을 생성한다. \n",
"\n",
"몇가지 힌드는 다음과 같다:\n",
"timeseries.FillMissing을 사용해서 분석을 돌리기 전에 결측값을 채워넣는다. 이런 방식으로 연속된 요소값 사이 시점이 일치한다.\n",
"Series.diff을 사용해서 연속된 요소 사이 차이를 계산한다.\n",
"reindex을 사용해서 데이터프레임을 미래로 연장한다.\n",
"fillna을 사용해서 예측한 값을 데이터프레임에 넣는다."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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xUQhKORJ44ZUX8OM77y3JA9msaN+N4QZ88v2fRDLpls8qkmxPj1wzdtKpqRFL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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xac99034c>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<matplotlib.figure.Figure at 0xac8b332c>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def PlotEwmaPredictions(daily, name):\n",
" \"\"\"\n",
" \"\"\"\n",
"\n",
" # use EWMA to estimate slopes\n",
" filled = timeseries.FillMissing(daily)\n",
" filled['slope'] = pandas.ewma(filled.ppg.diff(), span=180)\n",
" filled[-1:]\n",
"\n",
" # extract the last inter and slope\n",
" start = filled.index[-1]\n",
" inter = filled.ewma[-1]\n",
" slope = filled.slope[-1]\n",
"\n",
" # reindex the DataFrame, adding a year to the end\n",
" dates = pandas.date_range(filled.index.min(), \n",
" filled.index.max() + np.timedelta64(365, 'D'))\n",
" predicted = filled.reindex(dates)\n",
"\n",
" # generate predicted values and add them to the end\n",
" predicted['date'] = predicted.index\n",
" one_day = np.timedelta64(1, 'D')\n",
" predicted['days'] = (predicted.date - start) / one_day\n",
" predict = inter + slope * predicted.days\n",
" predicted.ewma.fillna(predict, inplace=True)\n",
"\n",
" # plot the actual values and predictions\n",
" thinkplot.Scatter(daily.ppg, alpha=0.1, label=name)\n",
" thinkplot.Plot(predicted.ewma)\n",
" thinkplot.Show(legend=False)\n",
"\n",
"PlotEwmaPredictions(daily, name) "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.10"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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