diff --git a/11_Inference.ipynb b/11_Inference.ipynb index 0892a1c3..b85d3c07 100644 --- a/11_Inference.ipynb +++ b/11_Inference.ipynb @@ -18,7 +18,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -304,11 +304,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 63, "metadata": { "hidden": true }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "1.7108820799094278" + ] + }, + "execution_count": 63, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "a = 0.05\n", "dof = 30-5-1\n", @@ -328,11 +339,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 64, "metadata": { "hidden": true }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "-1.7108820799094282" + ] + }, + "execution_count": 64, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "t_left = t.ppf(a, dof)\n", "t_left" @@ -349,11 +371,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 65, "metadata": { "hidden": true }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "2.063898561628021" + ] + }, + "execution_count": 65, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "t_both = t.ppf(1-a/2, dof)\n", "t_both" @@ -370,11 +403,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 66, "metadata": { "hidden": true }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "2.063898561628021" + ] + }, + "execution_count": 66, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "abs(t.ppf(a/2,dof))" ] @@ -413,11 +457,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "metadata": { "hidden": true }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "0.050000000000000044" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "1-t.cdf(t_right, dof) # t.cdfについてはscipy.statsを参照" ] @@ -434,11 +489,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "metadata": { "hidden": true }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "0.050000000000000024" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "t.cdf(t_left, dof)" ] @@ -455,11 +521,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, "metadata": { "hidden": true }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "0.05000000000000049" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "2*( 1-t.cdf(t_both, dof) )" ] @@ -481,7 +558,8 @@ "cell_type": "markdown", "metadata": { "heading_collapsed": true, - "hidden": true + "hidden": true, + "jp-MarkdownHeadingCollapsed": true }, "source": [ "### 回帰分析と$t$検定" @@ -507,14 +585,61 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 67, "metadata": { "hidden": true, "tags": [ "output_scroll" ] }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "name of dataset: gpa1\n", + "no of variables: 29\n", + "no of observations: 141\n", + "\n", + "+----------+--------------------------------+\n", + "| variable | label |\n", + "+----------+--------------------------------+\n", + "| age | in years |\n", + "| soph | =1 if sophomore |\n", + "| junior | =1 if junior |\n", + "| senior | =1 if senior |\n", + "| senior5 | =1 if fifth year senior |\n", + "| male | =1 if male |\n", + "| campus | =1 if live on campus |\n", + "| business | =1 if business major |\n", + "| engineer | =1 if engineering major |\n", + "| colGPA | MSU GPA |\n", + "| hsGPA | high school GPA |\n", + "| ACT | 'achievement' score |\n", + "| job19 | =1 if job <= 19 hours |\n", + "| job20 | =1 if job >= 20 hours |\n", + "| drive | =1 if drive to campus |\n", + "| bike | =1 if bicycle to campus |\n", + "| walk | =1 if walk to campus |\n", + "| voluntr | =1 if do volunteer work |\n", + "| PC | =1 of pers computer at sch |\n", + "| greek | =1 if fraternity or sorority |\n", + "| car | =1 if own car |\n", + "| siblings | =1 if have siblings |\n", + "| bgfriend | =1 if boy- or girlfriend |\n", + "| clubs | =1 if belong to MSU club |\n", + "| skipped | avg lectures missed per week |\n", + "| alcohol | avg # days per week drink alc. |\n", + "| gradMI | =1 if Michigan high school |\n", + "| fathcoll | =1 if father college grad |\n", + "| mothcoll | =1 if mother college grad |\n", + "+----------+--------------------------------+\n", + "\n", + "Christopher Lemmon, a former MSU undergraduate, collected these data\n", + "from a survey he took of MSU students in Fall 1994.\n" + ] + } + ], "source": [ "gpa = wooldridge.data('gpa1')\n", "wooldridge.data('gpa1',description=True)" @@ -534,7 +659,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 68, "metadata": { "hidden": true }, @@ -564,11 +689,26 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "hidden": true - }, - "outputs": [], + "execution_count": 69, + "metadata": { + "hidden": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Intercept 4.191039\n", + "hsGPA 4.396260\n", + "ACT 1.393319\n", + "skipped -3.196840\n", + "dtype: float64" + ] + }, + "execution_count": 69, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "res_gpa.tvalues" ] @@ -584,7 +724,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 78, "metadata": { "hidden": true }, @@ -619,11 +759,29 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "hidden": true - }, - "outputs": [], + "execution_count": 75, + "metadata": { + "hidden": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Help on function significance_check in module __main__:\n", + "\n", + "significance_check(res, a=0.05)\n", + " 定数項がある場合のt検定をおこなう。\n", + " \n", + " 引数：\n", + " res = statsmodelsによるOLS推定結果\n", + " a = 有意水準（デフォルト：0.05）\n", + " 返り値：\n", + " 帰無仮説を棄却する場合はTrueを返す。\n", + "\n" + ] + } + ], "source": [ "help(significance_check)" ] @@ -644,11 +802,26 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "hidden": true - }, - "outputs": [], + "execution_count": 76, + "metadata": { + "hidden": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Intercept True\n", + "hsGPA True\n", + "ACT False\n", + "skipped True\n", + "dtype: bool" + ] + }, + "execution_count": 76, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "significance_check(res_gpa, 0.05)" ] @@ -664,11 +837,26 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "hidden": true - }, - "outputs": [], + "execution_count": 77, + "metadata": { + "hidden": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Intercept 0.000050\n", + "hsGPA 0.000022\n", + "ACT 0.165780\n", + "skipped 0.001725\n", + "dtype: float64" + ] + }, + "execution_count": 77, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "res_gpa.pvalues" ] @@ -684,11 +872,26 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "hidden": true - }, - "outputs": [], + "execution_count": 57, + "metadata": { + "hidden": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "==============================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "------------------------------------------------------------------------------\n", + "Intercept 1.3896 0.332 4.191 0.000 0.734 2.045\n", + "hsGPA 0.4118 0.094 4.396 0.000 0.227 0.597\n", + "ACT 0.0147 0.011 1.393 0.166 -0.006 0.036\n", + "skipped -0.0831 0.026 -3.197 0.002 -0.135 -0.032\n", + "==============================================================================\n" + ] + } + ], "source": [ "print(res_gpa.summary().tables[1])" ] @@ -710,11 +913,26 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "hidden": true - }, - "outputs": [], + "execution_count": 58, + "metadata": { + "hidden": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Intercept 0.331554\n", + "hsGPA 0.093674\n", + "ACT 0.010565\n", + "skipped 0.025999\n", + "dtype: float64" + ] + }, + "execution_count": 58, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "res_gpa.bse" ] @@ -728,9 +946,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 116, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " t値\n", + "--------------------\n", + "Intercept 4.1910\n", + "hsGPA 4.3963\n", + "ACT 1.3933\n", + "skipped -3.1968\n" + ] + } + ], "source": [ "print(' '*15, 't値')\n", "print('-'*20)\n", @@ -749,14 +980,18 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "jp-MarkdownHeadingCollapsed": true + }, "source": [ "### 片側検定" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "jp-MarkdownHeadingCollapsed": true + }, "source": [ "#### `ACT`の場合" ] @@ -780,9 +1015,20 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 117, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "0.08288995083194341" + ] + }, + "execution_count": 117, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# 両側検定のp値\n", "p_ACT_two_tailed = res_gpa.pvalues['ACT']\n", @@ -813,16 +1059,29 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 119, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "0.9171100491680566" + ] + }, + "execution_count": 119, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "1 - p_ACT_two_tailed / 2" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "jp-MarkdownHeadingCollapsed": true + }, "source": [ "#### `skipped`の場合" ] @@ -841,9 +1100,20 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 121, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "0.0008627155651911229" + ] + }, + "execution_count": 121, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# 両側検定のp値\n", "p_skipped_two_tailed = res_gpa.pvalues['skipped']\n", @@ -857,16 +1127,31 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "$p$は更に小さくなっている。\n", + "両側検定と比べて$p$値は小さくなっている。\n", "\n", - "右側検定もおこなうことができるが，推定値が負の値になっていることを留意し，次のコードで$p$値を計算できる。" + "次の右側検定もおこなうことができる。\n", + "\n", + "$$H_A:\\hat{\\beta}_{\\text{skipped}}>0$$\n", + "\n", + "推定値が負の値になっていることを留意し，次のコードで$p$値を計算できる。" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 122, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "0.9991372844348089" + ] + }, + "execution_count": 122, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "1 - p_skipped_two_tailed / 2" ] @@ -950,11 +1235,23 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 18, "metadata": { "hidden": true }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0 1\n", + "Intercept 0.733930 2.045178\n", + "hsGPA 0.226582 0.597050\n", + "ACT -0.006171 0.035612\n", + "skipped -0.134523 -0.031703\n" + ] + } + ], "source": [ "print(res_gpa.conf_int())" ] @@ -970,11 +1267,23 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 19, "metadata": { "hidden": true }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0 1\n", + "Intercept 0.523472 2.255635\n", + "hsGPA 0.167121 0.656511\n", + "ACT -0.012877 0.042318\n", + "skipped -0.151026 -0.015200\n" + ] + } + ], "source": [ "print(res_gpa.conf_int(alpha=0.01))" ] @@ -1010,11 +1319,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 20, "metadata": { "hidden": true }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "coef = res_gpa.params # 推定値\n", "varname = coef.index # 変数名\n", @@ -1173,14 +1493,82 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 21, "metadata": { "hidden": true, "tags": [ "output_scroll" ] }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "name of dataset: mlb1\n", + "no of variables: 47\n", + "no of observations: 353\n", + "\n", + "+----------+----------------------------+\n", + "| variable | label |\n", + "+----------+----------------------------+\n", + "| salary | 1993 season salary |\n", + "| teamsal | team payroll |\n", + "| nl | =1 if national league |\n", + "| years | years in major leagues |\n", + "| games | career games played |\n", + "| atbats | career at bats |\n", + "| runs | career runs scored |\n", + "| hits | career hits |\n", + "| doubles | career doubles |\n", + "| triples | career triples |\n", + "| hruns | career home runs |\n", + "| rbis | career runs batted in |\n", + "| bavg | career batting average |\n", + "| bb | career walks |\n", + "| so | career strike outs |\n", + "| sbases | career stolen bases |\n", + "| fldperc | career fielding perc |\n", + "| frstbase | = 1 if first base |\n", + "| scndbase | =1 if second base |\n", + "| shrtstop | =1 if shortstop |\n", + "| thrdbase | =1 if third base |\n", + "| outfield | =1 if outfield |\n", + "| catcher | =1 if catcher |\n", + "| yrsallst | years as all-star |\n", + "| hispan | =1 if hispanic |\n", + "| black | =1 if black |\n", + "| whitepop | white pop. in city |\n", + "| blackpop | black pop. in city |\n", + "| hisppop | hispanic pop. in city |\n", + "| pcinc | city per capita income |\n", + "| gamesyr | games per year in league |\n", + "| hrunsyr | home runs per year |\n", + "| atbatsyr | at bats per year |\n", + "| allstar | perc. of years an all-star |\n", + "| slugavg | career slugging average |\n", + "| rbisyr | rbis per year |\n", + "| sbasesyr | stolen bases per year |\n", + "| runsyr | runs scored per year |\n", + "| percwhte | percent white in city |\n", + "| percblck | percent black in city |\n", + "| perchisp | percent hispanic in city |\n", + "| blckpb | black*percblck |\n", + "| hispph | hispan*perchisp |\n", + "| whtepw | white*percwhte |\n", + "| blckph | black*perchisp |\n", + "| hisppb | hispan*percblck |\n", + "| lsalary | log(salary) |\n", + "+----------+----------------------------+\n", + "\n", + "Collected by G. Mark Holmes, a former MSU undergraduate, for a term\n", + "project. The salary data were obtained from the New York Times, April\n", + "11, 1993. The baseball statistics are from The Baseball Encyclopedia,\n", + "9th edition, and the city population figures are from the Statistical\n", + "Abstract of the United States.\n" + ] + } + ], "source": [ "mlb1 = wooldridge.data('mlb1')\n", "wooldridge.data('mlb1',description=True)" @@ -1204,7 +1592,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 22, "metadata": { "hidden": true }, @@ -1249,7 +1637,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 23, "metadata": { "hidden": true }, @@ -1280,11 +1668,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 24, "metadata": { "hidden": true }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "9.550253521951914" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# 決定係数\n", "r2_0 = res_0.rsquared\n", @@ -1310,11 +1709,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 25, "metadata": { "hidden": true }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "2.6306414891156504" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "a = 0.05\n", "f.ppf(1-a, dfn=q, dfd=n-k-1) # f.ppfについてはscipy.statsを参照" @@ -1340,11 +1750,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 26, "metadata": { "hidden": true }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "4.473708139829391e-06" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "1-f.cdf(F, dfn=q, dfd=n-k-1)" ] @@ -1370,7 +1791,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 27, "metadata": { "hidden": true }, @@ -1390,7 +1811,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 28, "metadata": { "hidden": true }, @@ -1410,11 +1831,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 29, "metadata": { "hidden": true }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "''" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "res_f_test.summary()" ] @@ -1462,22 +1894,44 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 30, "metadata": { "hidden": true }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "117.06032008521446" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "res_0.fvalue" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 31, "metadata": { "hidden": true }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "2.938042293220727e-72" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "res_0.f_pvalue" ] @@ -1495,11 +1949,49 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "hidden": true - }, - "outputs": [], + "execution_count": 32, + "metadata": { + "hidden": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: np.log(salary) R-squared: 0.628\n", + "Model: OLS Adj. R-squared: 0.622\n", + "Method: Least Squares F-statistic: 117.1\n", + "Date: Sun, 21 Jul 2024 Prob (F-statistic): 2.94e-72\n", + "Time: 13:42:34 Log-Likelihood: -385.11\n", + "No. Observations: 353 AIC: 782.2\n", + "Df Residuals: 347 BIC: 805.4\n", + "Df Model: 5 \n", + "Covariance Type: nonrobust \n", + "==============================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "------------------------------------------------------------------------------\n", + "Intercept 11.1924 0.289 38.752 0.000 10.624 11.760\n", + "years 0.0689 0.012 5.684 0.000 0.045 0.093\n", + "gamesyr 0.0126 0.003 4.742 0.000 0.007 0.018\n", + "bavg 0.0010 0.001 0.887 0.376 -0.001 0.003\n", + "hrunsyr 0.0144 0.016 0.899 0.369 -0.017 0.046\n", + "rbisyr 0.0108 0.007 1.500 0.134 -0.003 0.025\n", + "==============================================================================\n", + "Omnibus: 6.816 Durbin-Watson: 1.265\n", + "Prob(Omnibus): 0.033 Jarque-Bera (JB): 10.197\n", + "Skew: -0.068 Prob(JB): 0.00610\n", + "Kurtosis: 3.821 Cond. No. 2.09e+03\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", + "[2] The condition number is large, 2.09e+03. This might indicate that there are\n", + "strong multicollinearity or other numerical problems.\n" + ] + } + ], "source": [ "print(res_0.summary())" ]