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HW.ipynb
{
"cells": [
{
"cell_type": "code",
"source": [
"import pandas as pd\n",
"import statsmodels.api as sm\n",
"from statsmodels.iolib.summary2 import summary_col\n",
"import ggplot"
],
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": [
"C:\\Program Files\\Anaconda3\\lib\\site-packages\\statsmodels\\compat\\pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
" from pandas.core import datetools\n",
"C:\\Program Files\\Anaconda3\\lib\\site-packages\\ggplot\\utils.py:81: FutureWarning: pandas.tslib is deprecated and will be removed in a future version.\n",
"You can access Timestamp as pandas.Timestamp\n",
" pd.tslib.Timestamp,\n",
"C:\\Program Files\\Anaconda3\\lib\\site-packages\\ggplot\\stats\\smoothers.py:4: FutureWarning: The pandas.lib module is deprecated and will be removed in a future version. These are private functions and can be accessed from pandas._libs.lib instead\n",
" from pandas.lib import Timestamp\n"
]
}
],
"execution_count": 1,
"metadata": {
"collapsed": false,
"outputHidden": false,
"inputHidden": false
}
},
{
"cell_type": "code",
"source": [
"art_museum_data = pd.read_excel(\"artmuseum.xlsx\")\n",
"art_museum_data.columns=[\"fee\",\"nh\",\"ne\",\"space\",\"year\",\"rail\",\"bus\",\"comp\",\"piif\",\"pub\",\"lib\",\"lec\",\"ws\",\"guide\",\"club\",\"private\",\"tokyo\"]"
],
"outputs": [],
"execution_count": 2,
"metadata": {
"collapsed": false,
"outputHidden": false,
"inputHidden": false
}
},
{
"cell_type": "code",
"source": [
"X = art_museum_data.loc[:,\"nh\":\"tokyo\"]\n",
"Y = art_museum_data.loc[:,\"fee\"]"
],
"outputs": [],
"execution_count": 3,
"metadata": {
"collapsed": false,
"outputHidden": false,
"inputHidden": false
}
},
{
"cell_type": "code",
"source": [
"X = sm.add_constant(X) # adding a constant\n",
"model = sm.OLS(Y, X)\n",
"res = model.fit()\n",
"print(res.summary())\n",
"# here the conditional number is very big, indicating strong instability of the model"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: fee R-squared: 0.771\n",
"Model: OLS Adj. R-squared: 0.578\n",
"Method: Least Squares F-statistic: 3.990\n",
"Date: Sat, 26 Jan 2019 Prob (F-statistic): 0.00251\n",
"Time: 14:10:44 Log-Likelihood: -232.78\n",
"No. Observations: 36 AIC: 499.6\n",
"Df Residuals: 19 BIC: 526.5\n",
"Df Model: 16 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"const 3453.0041 3259.777 1.059 0.303 -3369.787 1.03e+04\n",
"nh -0.0038 0.003 -1.219 0.238 -0.010 0.003\n",
"ne 0.6252 0.737 0.848 0.407 -0.917 2.168\n",
"space 0.0168 0.005 3.672 0.002 0.007 0.026\n",
"year -1.0351 1.630 -0.635 0.533 -4.446 2.376\n",
"rail 330.2386 165.396 1.997 0.060 -15.940 676.417\n",
"bus -120.6369 122.653 -0.984 0.338 -377.352 136.078\n",
"comp -326.4530 202.917 -1.609 0.124 -751.163 98.257\n",
"piif -249.1368 154.648 -1.611 0.124 -572.818 74.545\n",
"pub -601.5254 172.905 -3.479 0.003 -963.419 -239.632\n",
"lib 132.4595 144.636 0.916 0.371 -170.267 435.186\n",
"lec 30.7109 143.474 0.214 0.833 -269.584 331.006\n",
"ws -28.8792 110.058 -0.262 0.796 -259.233 201.475\n",
"guide -460.0881 192.169 -2.394 0.027 -862.302 -57.875\n",
"club 135.0211 130.438 1.035 0.314 -137.989 408.031\n",
"private -165.2505 189.250 -0.873 0.393 -561.355 230.854\n",
"tokyo 43.9299 152.037 0.289 0.776 -274.287 362.146\n",
"==============================================================================\n",
"Omnibus: 1.556 Durbin-Watson: 1.890\n",
"Prob(Omnibus): 0.459 Jarque-Bera (JB): 1.047\n",
"Skew: -0.039 Prob(JB): 0.592\n",
"Kurtosis: 2.168 Cond. No. 2.20e+06\n",
"==============================================================================\n",
"\n",
"Warnings:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"[2] The condition number is large, 2.2e+06. This might indicate that there are\n",
"strong multicollinearity or other numerical problems.\n"
]
}
],
"execution_count": 4,
"metadata": {
"collapsed": false,
"outputHidden": false,
"inputHidden": false
}
},
{
"cell_type": "markdown",
"source": [
"# 模型的理论构建\n",
"- $$Y(fee) = X\\beta+\\epsilon=1*\\beta_0+nh*\\beta_1+ne*\\beta_2+...+tokyo*\\beta_{16}+\\epsilon $$\n",
"- $\\beta=\\partial{fee}/\\partial{x}$:x每增加一单位，对应的费用增加或者减少$\\beta$元。\n"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"# 解读回归结果\n",
"- 首先，可以明显的看到space的系数在0.5%的水平上显著为正（P>|t|即p-value小于0.5%，三颗星），数量上即每增加一平方米，收费增加0.0168日元。\n",
"- 其次，公立（pub）的博物馆收费显著（P-value小于0.5%，三颗星）低于非公立博物馆，平均价格下降600日元左右。\n",
"- 再次，有guide的博物馆在收费上低于其他，显著性一颗星（P=0.027在5%水平显著，1颗星）。这个很难解释\n",
"- 最后，$R^2=\\frac{SSR}{SST}=1-\\frac{SSE}{SST}$ 和 Adj$R^2=1-(\\frac{n-1}{n-p})(\\frac{SSE}{SST})$,其中R^2表明了加入的解释变量在多大程度解释了被解释变量的变化。AdjR^2进一步加入了解释变量的数量的惩罚项，衡量了在控制解释变量数量的情况下，解释变量多大程度上解释了被解释变量。其中R^2为70%多，adjR^2为60%左右，还是比较高的。\n",
"- 所有解释变量都参与，AIC 为499"
],
"metadata": {
"collapsed": false,
"outputHidden": false,
"inputHidden": false
}
},
{
"cell_type": "markdown",
"source": [
"# 尝试解释为什么guide的值为负\n",
"## 猜想1：guide可能和其他变量有相关性，比如pub，猜想公立博物馆有guide的比重更高"
],
"metadata": {}
},
{
"cell_type": "code",
"source": [
"\n",
"### 公立博物馆中有guide的比重\n",
"guide_1=X['guide'][X['pub']==1].count()\n",
"guide_2=X['guide'][X['pub']==1].sum()\n",
"guide_pub = guide_2/guide_1\n",
"### 非公立博物馆中有guide的比重\n",
"guide_11 = X['guide'][X['pub']==0].count()\n",
"guide_21 = X['guide'][X['pub']==0].sum()\n",
"guide_non_pub = guide_21/guide_11\n",
"print(guide_pub,guide_non_pub)\n",
"\n"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.8 0.875\n"
]
},
{
"output_type": "error",
"ename": "TypeError",
"evalue": "corr() missing 1 required positional argument: 'other'",
"traceback": [
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[1;31mTypeError\u001b[0m Traceback (most recent call last)",
"\u001b[1;32m<ipython-input-40-b8cc5278261c>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m 13\u001b[0m \u001b[1;31m# 结果差不多，否决\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 14\u001b[0m \u001b[1;31m### 尝试2：查看guide和其他解释变量的相关性\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 15\u001b[1;33m \u001b[0mX\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpub\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcorr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[1;31mTypeError\u001b[0m: corr() missing 1 required positional argument: 'other'"
]
}
],
"execution_count": 40,
"metadata": {
"collapsed": false,
"outputHidden": false,
"inputHidden": false
}
},
{
"cell_type": "markdown",
"source": [
"# 0.8 0.875\n",
"# 结果差不多，否决"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"# 尝试2：查看guide和其他解释变量的相关性\n",
"- 2.1 尝试相关系数correlation\n",
"- 2.2 使用guide作为被解释变量，其他变量为解释变量，挑选出显著并且比较大的系数的变量，在下次回归当中删除。"
],
"metadata": {}
},
{
"cell_type": "code",
"source": [
"### 尝试2.1：查看guide和其他解释变量的相关性\n",
"pub_cor = [X.pub.corr(X[i]) for i in X.columns]\n",
"Possible_corr_var = [X.columns[i] for i in range(15) if pub_cor[i]>0.4]\n",
"print(Possible_corr_var)\n",
"## 2.2 使用线性概率模型，查看那些变量显著影响了guide，下次从回归当中删除。\n",
"model_guide = sm.OLS(X.guide,X.iloc[:,X.columns!='guide']).fit().summary()\n",
"print(model_guide)\n",
"##看到 系数比较大并且比较显著的影响guide的变量为['club','lib','rail']"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"['ne', 'space', 'pub', 'lib']\n",
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: guide R-squared: 0.752\n",
"Model: OLS Adj. R-squared: 0.565\n",
"Method: Least Squares F-statistic: 4.034\n",
"Date: Sat, 26 Jan 2019 Prob (F-statistic): 0.00217\n",
"Time: 17:07:44 Log-Likelihood: 9.5210\n",
"No. Observations: 36 AIC: 12.96\n",
"Df Residuals: 20 BIC: 38.29\n",
"Df Model: 15 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"const 5.0422 3.622 1.392 0.179 -2.512 12.597\n",
"nh -6.271e-06 3.39e-06 -1.848 0.080 -1.34e-05 8.09e-07\n",
"ne 0.0003 0.001 0.404 0.690 -0.001 0.002\n",
"space -1.107e-05 4.72e-06 -2.345 0.029 -2.09e-05 -1.22e-06\n",
"year -0.0024 0.002 -1.339 0.196 -0.006 0.001\n",
"rail 0.5902 0.140 4.213 0.000 0.298 0.882\n",
"bus 0.3023 0.126 2.405 0.026 0.040 0.564\n",
"comp -0.2342 0.230 -1.017 0.321 -0.714 0.246\n",
"piif -0.3642 0.160 -2.269 0.034 -0.699 -0.029\n",
"pub -0.4317 0.177 -2.446 0.024 -0.800 -0.063\n",
"lib 0.5158 0.123 4.208 0.000 0.260 0.771\n",
"lec -0.0249 0.167 -0.149 0.883 -0.373 0.323\n",
"ws 0.1129 0.126 0.899 0.379 -0.149 0.375\n",
"club 0.3173 0.134 2.365 0.028 0.037 0.597\n",
"private -0.0606 0.220 -0.276 0.786 -0.519 0.398\n",
"tokyo 0.2229 0.170 1.313 0.204 -0.131 0.577\n",
"==============================================================================\n",
"Omnibus: 0.236 Durbin-Watson: 1.786\n",
"Prob(Omnibus): 0.889 Jarque-Bera (JB): 0.042\n",
"Skew: -0.082 Prob(JB): 0.979\n",
"Kurtosis: 2.965 Cond. No. 2.10e+06\n",
"==============================================================================\n",
"\n",
"Warnings:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"[2] The condition number is large, 2.1e+06. This might indicate that there are\n",
"strong multicollinearity or other numerical problems.\n"
]
}
],
"execution_count": 106,
"metadata": {
"collapsed": false,
"outputHidden": false,
"inputHidden": false
}
},
{
"cell_type": "markdown",
"source": [
"## 下面尝试把这些变量删掉看会不会影响guide的显著性"
],
"metadata": {}
},
{
"cell_type": "code",
"source": [
"### 继续尝试2.1，尝试删掉和guide共线性比较大的变量然后回归\n",
"model2 = sm.OLS(Y, X.iloc[:,~X.columns.isin(Possible_corr_var)])\n",
"res2 = model2.fit()\n",
"print(res2.summary())\n",
"# 回归结果R^2下降严重，AIC上升较大，所以这一方法不可取，放弃\n"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: fee R-squared: 0.413\n",
"Model: OLS Adj. R-squared: 0.106\n",
"Method: Least Squares F-statistic: 1.346\n",
"Date: Sat, 26 Jan 2019 Prob (F-statistic): 0.260\n",
"Time: 17:08:19 Log-Likelihood: -249.71\n",
"No. Observations: 36 AIC: 525.4\n",
"Df Residuals: 23 BIC: 546.0\n",
"Df Model: 12 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"const 6526.6179 4260.828 1.532 0.139 -2287.576 1.53e+04\n",
"nh 0.0014 0.004 0.346 0.733 -0.007 0.010\n",
"year -2.7408 2.139 -1.281 0.213 -7.165 1.684\n",
"rail 255.3356 185.842 1.374 0.183 -129.109 639.780\n",
"bus -111.6011 162.732 -0.686 0.500 -448.239 225.036\n",
"comp 185.7578 183.966 1.010 0.323 -194.806 566.321\n",
"piif 69.1083 144.591 0.478 0.637 -230.000 368.217\n",
"lec 156.4431 202.753 0.772 0.448 -262.984 575.870\n",
"ws 37.6614 125.003 0.301 0.766 -220.926 296.249\n",
"guide -381.7440 178.043 -2.144 0.043 -750.054 -13.434\n",
"club 25.1796 159.059 0.158 0.876 -303.859 354.218\n",
"private -298.1011 271.183 -1.099 0.283 -859.086 262.884\n",
"tokyo -49.7687 201.684 -0.247 0.807 -466.985 367.447\n",
"==============================================================================\n",
"Omnibus: 0.208 Durbin-Watson: 1.941\n",
"Prob(Omnibus): 0.901 Jarque-Bera (JB): 0.038\n",
"Skew: -0.075 Prob(JB): 0.981\n",
"Kurtosis: 2.950 Cond. No. 1.68e+06\n",
"==============================================================================\n",
"\n",
"Warnings:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"[2] The condition number is large, 1.68e+06. This might indicate that there are\n",
"strong multicollinearity or other numerical problems.\n",
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: fee R-squared: 0.720\n",
"Model: OLS Adj. R-squared: 0.554\n",
"Method: Least Squares F-statistic: 4.344\n",
"Date: Sat, 26 Jan 2019 Prob (F-statistic): 0.00124\n",
"Time: 17:08:19 Log-Likelihood: -236.40\n",
"No. Observations: 36 AIC: 500.8\n",
"Df Residuals: 22 BIC: 523.0\n",
"Df Model: 13 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"const 2586.9108 3180.851 0.813 0.425 -4009.771 9183.592\n",
"nh -0.0019 0.003 -0.688 0.499 -0.008 0.004\n",
"ne 0.8677 0.718 1.208 0.240 -0.622 2.357\n",
"space 0.0199 0.004 4.830 0.000 0.011 0.028\n",
"year -0.6063 1.600 -0.379 0.708 -3.925 2.712\n",
"bus -221.9872 112.812 -1.968 0.062 -455.944 11.970\n",
"comp -226.8406 185.080 -1.226 0.233 -610.673 156.992\n",
"piif -85.5670 124.392 -0.688 0.499 -343.540 172.406\n",
"pub -456.0002 143.674 -3.174 0.004 -753.963 -158.038\n",
"lec 19.8057 129.767 0.153 0.880 -249.315 288.927\n",
"ws -58.8600 102.880 -0.572 0.573 -272.219 154.499\n",
"guide -212.0717 124.662 -1.701 0.103 -470.605 46.461\n",
"private -107.3435 187.088 -0.574 0.572 -495.341 280.654\n",
"tokyo 55.8507 135.820 0.411 0.685 -225.823 337.524\n",
"==============================================================================\n",
"Omnibus: 0.285 Durbin-Watson: 1.756\n",
"Prob(Omnibus): 0.867 Jarque-Bera (JB): 0.472\n",
"Skew: 0.055 Prob(JB): 0.790\n",
"Kurtosis: 2.450 Cond. No. 2.09e+06\n",
"==============================================================================\n",
"\n",
"Warnings:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"[2] The condition number is large, 2.09e+06. This might indicate that there are\n",
"strong multicollinearity or other numerical problems.\n"
]
}
],
"execution_count": 107,
"metadata": {
"collapsed": false,
"outputHidden": false,
"inputHidden": false
}
},
{
"cell_type": "code",
"source": [
"### 继续尝试2.2\n",
"model3 = sm.OLS(Y, X.iloc[:,~X.columns.isin(['club','lib','rail'])])\n",
"res3 = model3.fit()\n",
"print(res3.summary())\n",
"# 回归结果R^2基本不变，并且看到AIC也基本没有变，所以模型的解释力没有大的变化，但是这里guide变得不显著了，所以我们无法对guide做肯定判断，但是space和pub的结果是稳定的。"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: fee R-squared: 0.720\n",
"Model: OLS Adj. R-squared: 0.554\n",
"Method: Least Squares F-statistic: 4.344\n",
"Date: Sat, 26 Jan 2019 Prob (F-statistic): 0.00124\n",
"Time: 17:20:33 Log-Likelihood: -236.40\n",
"No. Observations: 36 AIC: 500.8\n",
"Df Residuals: 22 BIC: 523.0\n",
"Df Model: 13 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"const 2586.9108 3180.851 0.813 0.425 -4009.771 9183.592\n",
"nh -0.0019 0.003 -0.688 0.499 -0.008 0.004\n",
"ne 0.8677 0.718 1.208 0.240 -0.622 2.357\n",
"space 0.0199 0.004 4.830 0.000 0.011 0.028\n",
"year -0.6063 1.600 -0.379 0.708 -3.925 2.712\n",
"bus -221.9872 112.812 -1.968 0.062 -455.944 11.970\n",
"comp -226.8406 185.080 -1.226 0.233 -610.673 156.992\n",
"piif -85.5670 124.392 -0.688 0.499 -343.540 172.406\n",
"pub -456.0002 143.674 -3.174 0.004 -753.963 -158.038\n",
"lec 19.8057 129.767 0.153 0.880 -249.315 288.927\n",
"ws -58.8600 102.880 -0.572 0.573 -272.219 154.499\n",
"guide -212.0717 124.662 -1.701 0.103 -470.605 46.461\n",
"private -107.3435 187.088 -0.574 0.572 -495.341 280.654\n",
"tokyo 55.8507 135.820 0.411 0.685 -225.823 337.524\n",
"==============================================================================\n",
"Omnibus: 0.285 Durbin-Watson: 1.756\n",
"Prob(Omnibus): 0.867 Jarque-Bera (JB): 0.472\n",
"Skew: 0.055 Prob(JB): 0.790\n",
"Kurtosis: 2.450 Cond. No. 2.09e+06\n",
"==============================================================================\n",
"\n",
"Warnings:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"[2] The condition number is large, 2.09e+06. This might indicate that there are\n",
"strong multicollinearity or other numerical problems.\n"
]
}
],
"execution_count": 108,
"metadata": {
"collapsed": false,
"outputHidden": false,
"inputHidden": false
}
},
{
"cell_type": "markdown",
"source": [
"# 2.2 稳健性检验的解读（针对guide这一变量）\n",
"回归结果R^2基本不变，并且看到AIC也基本没有变，所以模型的解释力没有大的变化，但是这里guide变得不显著了，所以我们无法对guide做肯定判断，但是space和pub的结果是稳定的。"
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"# 可能的问题及方法\n",
"- 数据不足：1. 样本量太少，只有36个，可以增加调查范围或者扩大搜集博物馆的地域范围 2.其他解释变量数量不足。\n",
"- 可能的解释变量：\n",
"- A:博物馆定价方面（供给侧）1. 从博物馆的性质出发，可以看到公立博物馆收费低廉，如果进一步知道政府对公立博物馆的补贴数量和比重，可以更精确的解释为什么公立博物馆更加低廉。2. 另外，从成本出发，如果知道博物馆雇佣的员工数，工资总额及文物的修缮保养费用及其他运营费用的话可以增进分析。3. 周边环境，考虑到如果周边博物馆或者艺术馆有集聚（如北京798艺术区），受众出行到这一博物馆参观的概率会增加。\n",
"- B:需求方面。1. 博物馆的受众的特征，如年龄，兴趣，性别，收入等，这些变量会决定受众的支付意愿。2. 潜在的受众数量（市场大小），例如可以找到社交媒体上的#XX博物馆的帖子的数量和热度来作为相关的变量。\n",
"- C: 博物馆的所属种类（博物馆属于哪个市场？）：例如动漫博物馆和传统的艺术博物馆几乎不存在竞争性，不应放在一起考量，搜集博物馆所属门类的变量有助于建立更为细致的模型。"
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