{"id":5052,"date":"2022-11-21T14:33:26","date_gmt":"2022-11-21T06:33:26","guid":{"rendered":"https:\/\/seit2019.xyz\/?p=5052"},"modified":"2022-11-28T14:36:33","modified_gmt":"2022-11-28T06:36:33","slug":"5-5-%e8%ae%a1%e9%87%8f%e5%ae%9e%e9%aa%8c5%ef%bc%9a%e5%a4%9a%e9%87%8d%e5%85%b1%e7%ba%bf%e6%80%a7%e7%9a%84%e8%af%8a%e6%96%ad%e4%b8%8e%e5%a4%84%e7%90%86","status":"publish","type":"post","link":"https:\/\/seit2019.xyz\/?p=5052","title":{"rendered":"5.5 \u8ba1\u91cf\u5206\u67905\uff1a\u591a\u91cd\u5171\u7ebf\u6027\u7684\u8bca\u65ad\u4e0e\u5904\u7406"},"content":{"rendered":"

\u4f8b\u5b50\uff1a<\/h3>\n

\"\u886810.8\"<\/p>\n

\u4ee3\u7801\u90e8\u5206<\/h3>\n
# lec05\n# \u8ba1\u91cf\u5b9e\u9a8c3-\u4ee3\u7801\u90e8\u5206-02 \u591a\u91cd\u5171\u7ebf\u6027\u7684\u8bca\u65ad\u4e0e\u5904\u7406\n\n# \u5bfc\u5165\u5e93\u6587\u4ef6\nimport pandas as pd\nimport statsmodels.api as sm\nfrom statsmodels.stats.outliers_influence import variance_inflation_factor\nimport ssl\n\n# \u7981\u7528SSL\u8bc1\u4e66\u6821\u9a8c\nssl._create_default_https_context = ssl._create_unverified_context# \u5bfc\u5165\u5728\u7ebf\u6570\u636e\n\n# \u5bfc\u5165\u5728\u7ebf\u6570\u636e\ndf = pd.read_excel(r"https:\/\/cdn.seit2019.xyz\/data\/econometrics\/table10.8.xlsx")\n\n# \u5c55\u793a\u6570\u636e\nprint("\u539f\u59cb\u6570\u636e\u5c55\u793a\u5982\u4e0b\uff1a")\nprint(df, "\\n")\n\n# \u7b80\u8981\u7684\u63cf\u8ff0\u6027\u7edf\u8ba1\nprint("\u539f\u59cb\u6570\u636e\u7684\u4e3b\u8981\u7edf\u8ba1\u6307\u6807\uff1a")\nprint(df.describe(), "\\n")\n\n# \u591a\u5143\u7ebf\u6027\u56de\u5f52\n\n# \u4e3b\u56de\u5f52\u6a21\u578b\ny = df.Y\nx = df.iloc[:, 2:8]\nX = sm.add_constant(x)                            # \u6dfb\u52a0\u5e38\u6570\u9879\nOLS_model = sm.OLS(y, X).fit()                    # OLS\u56de\u5f52\nprint(OLS_model.summary(), "\\n")                  # \u663e\u793aOLS\u56de\u5f52\u7ed3\u679c\nR2 = OLS_model.rsquared                           # \u83b7\u53d6\u56de\u5f52R\u5e73\u65b9\ndfc = pd.DataFrame(OLS_model.params).round(4)     # \u83b7\u53d6\u56de\u5f52\u53c2\u6570,\u4fdd\u7559\u5c0f\u6570\u70b9\u540e4\u4f4d\ndfc = dfc.astype("string")                        # \u8f6c\u6362\u683c\u5f0f\u4e3a\u5b57\u7b26\u4e32\nbeta0 = dfc.iloc[0, 0]                            # \u5b9a\u4e49beta0\nbeta1 = dfc.iloc[1, 0]                            # \u5b9a\u4e49beta1\nbeta2 = dfc.iloc[2, 0]                            # \u5b9a\u4e49beta2\nbeta3 = dfc.iloc[3, 0]                            # \u5b9a\u4e49beta3\nbeta4 = dfc.iloc[4, 0]                            # \u5b9a\u4e49beta4\nbeta5 = dfc.iloc[5, 0]                            # \u5b9a\u4e49beta5\nbeta6 = dfc.iloc[6, 0]                            # \u5b9a\u4e49beta6\nOLS_equation = "Y=" + beta0 + beta1 + "*X1" + beta2 + "*X2" + beta3 + "*X3"+ beta4 + "*X4" + "+" + beta5 + "*X5" + "+" + beta6 + "*X6" # \u5b9a\u4e49\u56de\u5f52\u65b9\u7a0b\uff0c\u683c\u5f0f\uff1a\u5b57\u7b26\u4e32\nprint("\u4f30\u8ba1\u7684\u56de\u5f52\u65b9\u7a0b\u4e3a\uff1a")\nprint(OLS_equation, "\\n")\n# \u591a\u91cd\u5171\u7ebf\u6027\u8bca\u65ad\u539f\u52191\nprint("\u591a\u91cd\u5171\u7ebf\u6027\u8bca\u65ad\u539f\u52191\uff1a\u9ad8\u7684R\u5e73\u65b9\uff0c\u4f4e\u7684t\u503c", "\\n")\nprint("\u7ed3\u8bba\uff1a\u4e0a\u8ff0\u56de\u5f52\u7ed3\u679c\u4e2dR\u5e73\u65b9\uff080.995512\uff09\u5f88\u9ad8\uff0c\u4f46\u662f\u90e8\u5206\u53d8\u91cf\uff08X1,X2,X5\uff09\u7cfb\u6570\u4e0d\u663e\u8457\uff0c\u53ef\u80fd\u5b58\u5728\u591a\u91cd\u5171\u7ebf\u6027", "\\n")\n\n# \u76f8\u5173\u7cfb\u6570\u77e9\u9635\nx_corr = x.corr()\nprint(x_corr, "\\n")\n# \u76f8\u5173\u7cfb\u6570\u7b5b\u9009\ndf_x_corr =pd.DataFrame(x_corr)\ncorr1 = []\ncorr2 = []\nfor i in df_x_corr.index:\n    for j in df_x_corr.columns:\n        if i != j:\n            if df_x_corr.loc[i, j] >= 0.9:\n                corr1.append([i])\n                corr1.append([j])\n            elif df_x_corr.loc[i, j] > 0.6:\n                corr2.append([i])\n                corr2.append([j])\ndf_corr1 = pd.DataFrame(corr1)\ndf_corr2 = pd.DataFrame(corr2)\nfd1 = pd.unique(df_corr1[0])\nfd2 = pd.unique(df_corr2[0])\nprint("\u5b58\u5728\u9ad8\u5ea6\u76f8\u5173(r>0.9)\u7684\u89e3\u91ca\u53d8\u91cf\u6709\uff1a")\nfor x in fd1:\n    print(x)\nprint("\u5b58\u5728\u8f83\u9ad8\u76f8\u5173(r>0.6)\u7684\u89e3\u91ca\u53d8\u91cf\u6709\uff1a")\nfor x in fd2:\n    print(x)\n\n# \u591a\u91cd\u5171\u7ebf\u6027\u8bca\u65ad\u539f\u52192\nprint("\u591a\u91cd\u5171\u7ebf\u6027\u8bca\u65ad\u539f\u52192\uff1a\u89e3\u91ca\u53d8\u91cf\u4e4b\u95f4\u9ad8\u5ea6\u76f8\u5173\u6027\u3002")\nprint("\u7ed3\u8bba\uff1a\u6839\u636e\u4e0a\u8ff0\u89e3\u91ca\u53d8\u91cf\u7684\u76f8\u5173\u7cfb\u6570\u77e9\u9635\uff0c\u89e3\u91ca\u53d8\u91cfX1\u3001X2\u3001X5\u3001X6\u4e4b\u95f4\u5b58\u5728\u5f88\u9ad8\u7684\u76f8\u5173\u6027\uff08\u76f8\u5173\u7cfb\u6570\u5927\u4e8e0.9\uff09\uff0cX3\u3001X5\u3001X6\u4e4b\u95f4\u5b58\u5728\u8f83\u9ad8\u7684\u76f8\u5173\u6027\uff08\u76f8\u5173\u7cfb\u6570\u5927\u4e8e0.6\uff09\uff0c\u8fd9\u8868\u660e\u4e0a\u8ff0\u89e3\u91ca\u53d8\u91cf\u4e4b\u95f4\u53ef\u80fd\u5b58\u5728\u591a\u91cd\u5171\u7ebf\u6027\u3002", "\\n")\n\n# \u8f85\u52a9\u56de\u5f52\n# \u8f85\u52a9\u56de\u5f52\u6a21\u578b1\ny = df.X1\nx = df[["X2", "X3", "X4", "X5", "X6"]]\nX = sm.add_constant(x)                              # \u6dfb\u52a0\u5e38\u6570\u9879\nAUX_model1 = sm.OLS(y, X).fit()                     # OLS\u56de\u5f52\nprint(AUX_model1.summary(), "\\n")                   # \u663e\u793aOLS\u56de\u5f52\u7ed3\u679c\nR2_AUX1 = AUX_model1.rsquared                       # \u83b7\u53d6R\u5e73\u65b9\n\n# \u8f85\u52a9\u56de\u5f52\u6a21\u578b2\ny = df.X2\nx = df[["X1", "X3", "X4", "X5", "X6"]]\nX = sm.add_constant(x)                              # \u6dfb\u52a0\u5e38\u6570\u9879\nAUX_model2 = sm.OLS(y, X).fit()                     # OLS\u56de\u5f52\nprint(AUX_model2.summary(), "\\n")                   # \u663e\u793aOLS\u56de\u5f52\u7ed3\u679c\nR2_AUX2 = AUX_model2.rsquared                       # \u83b7\u53d6R\u5e73\u65b9\n# \u8f85\u52a9\u56de\u5f52\u6a21\u578b3\ny = df.X3\nx = df[["X1", "X2", "X4", "X5", "X6"]]\nX = sm.add_constant(x)                              # \u6dfb\u52a0\u5e38\u6570\u9879\nAUX_model3 = sm.OLS(y, X).fit()                     # OLS\u56de\u5f52\nprint(AUX_model3.summary(), "\\n")                   # \u663e\u793aOLS\u56de\u5f52\u7ed3\u679c\nR2_AUX3 = AUX_model3.rsquared                       # \u83b7\u53d6R\u5e73\u65b9\n# \u8f85\u52a9\u56de\u5f52\u6a21\u578b4\ny = df.X4\nx = df[["X1", "X2", "X3", "X5", "X6"]]\nX = sm.add_constant(x)                              # \u6dfb\u52a0\u5e38\u6570\u9879\nAUX_model4 = sm.OLS(y, X).fit()                     # OLS\u56de\u5f52\nprint(AUX_model4.summary(), "\\n")                   # \u663e\u793aOLS\u56de\u5f52\u7ed3\u679c\nR2_AUX4 = AUX_model4.rsquared                       # \u83b7\u53d6R\u5e73\u65b9\n# \u8f85\u52a9\u56de\u5f52\u6a21\u578b5\ny = df.X5\nx = df[["X1", "X2", "X3", "X4", "X6"]]\nX = sm.add_constant(x)                              # \u6dfb\u52a0\u5e38\u6570\u9879\nAUX_model5 = sm.OLS(y, X).fit()                     # OLS\u56de\u5f52\nprint(AUX_model5.summary(), "\\n")                   # \u663e\u793aOLS\u56de\u5f52\u7ed3\u679c\nR2_AUX5 = AUX_model5.rsquared                       # \u83b7\u53d6R\u5e73\u65b9\n# \u8f85\u52a9\u56de\u5f52\u6a21\u578b6\ny = df.X6\nx = df[["X1", "X2", "X3", "X4", "X5"]]\nX = sm.add_constant(x)                              # \u6dfb\u52a0\u5e38\u6570\u9879\nAUX_model6 = sm.OLS(y, X).fit()                     # OLS\u56de\u5f52\nprint(AUX_model6.summary(), "\\n")                   # \u663e\u793aOLS\u56de\u5f52\u7ed3\u679c\nR2_AUX6 = AUX_model6.rsquared                       # \u83b7\u53d6R\u5e73\u65b9\n\ndf_aux = pd.DataFrame(columns=["\u8f85\u52a9\u56de\u5f52", "\u88ab\u89e3\u91ca\u53d8\u91cf", "\u8f85\u52a9\u56de\u5f52R\u5e73\u65b9", "VIF\u503c", "TOL\u503c"])\ndata = {"\u8f85\u52a9\u56de\u5f52": ["1", "2", "3", "4", "5", "6"], "\u88ab\u89e3\u91ca\u53d8\u91cf": ["X1", "X2", "X3", "X4", "X5", "X6"]}\ndf_aux = pd.DataFrame(data)\ndf_aux["\u8f85\u52a9\u56de\u5f52R\u5e73\u65b9"] = pd.DataFrame([R2_AUX1, R2_AUX2, R2_AUX3, R2_AUX4, R2_AUX5, R2_AUX6]).round(4)\ndf_aux = df_aux.set_index("\u8f85\u52a9\u56de\u5f52")\nprint("\u8f85\u52a9\u56de\u5f52\u7684R\u5e73\u65b9\u4e3a\uff1a")\nprint(df_aux, "\\n")\n\n# \u8f85\u52a9\u56de\u5f52R\u5e73\u65b9\u4e0e\u4e3b\u56de\u5f52R\u5e73\u65b9\u6bd4\u8f83\nxvar = []\nfor i in range(6):\n    if df_aux.iloc[i, 1] > R2:\n        xvar.append(["X" + str(i+1)])\ndf_xvar = pd.DataFrame(xvar)\nprint("\u8f85\u52a9\u56de\u5f52R\u5e73\u65b9\u5927\u4e8e\u4e3b\u56de\u5f52\u7684R\u5e73\u65b9\u7684\u89e3\u91ca\u53d8\u91cf\u6709\uff1a")\nfor x in df_xvar[0]:\n    print(x)\n\n# \u591a\u91cd\u5171\u7ebf\u6027\u8bca\u65ad\u539f\u52193\nprint("\u591a\u91cd\u5171\u7ebf\u6027\u8bca\u65ad\u539f\u52193\uff1a\u89e3\u91ca\u53d8\u91cf\u4e4b\u95f4\u7684\u8f85\u52a9\u56de\u5f52R\u5e73\u65b9\u5927\u4e8e\u4e3b\u56de\u5f52\u7684R\u5e73\u65b9\u3002")\nprint("\u7ed3\u8bba\uff1a\u4ece\u4e0a\u8ff0\u8f85\u52a9\u56de\u5f52\u7ed3\u679c\u6765\u770b\uff0c\u89e3\u91ca\u53d8\u91cfX2\u3001X5\u3001X6\u5bf9\u5e94\u7684\u8f85\u52a9\u56de\u5f52R\u5e73\u65b9\u5927\u4e8e\u4e3b\u56de\u5f52\u7684R\u5e73\u65b9\uff0c\u8fd9\u8868\u660e\uff1a\u89e3\u91ca\u53d8\u91cfX2\u3001X5\u3001X6\u53ef\u80fd\u5f15\u53d1\u7684\u591a\u91cd\u5171\u7ebf\u6027", "\\n")\n\n# VIF\u548cTOL\u503c\n# \u5b9a\u4e49\u53d8\u91cf\ny = df.Y\nx = df.iloc[:, 2:8]\n# \u6dfb\u52a0\u5e38\u6570\u9879\nX = sm.add_constant(x)\n# \u8ba1\u7b97VIF\u503c\nprint("\u8f85\u52a9\u56de\u5f52\u7684R\u5e73\u65b9\uff0cTOL\u503c\u548cVIF\u503c\uff1a")\nvif_value = []\ntol_value = []\nfor i in range(6):\n    i += 1\n    vif = variance_inflation_factor(X.values, i)\n    tol = 1\/vif\n    vif_value.append(vif.round(2))\n    tol_value.append(tol.round(4))\ndf_aux["VIF\u503c"] = vif_value\ndf_aux["TOL\u503c"] = tol_value\nprint(df_aux, "\\n")\n# \u5224\u65adVIF\u503c\u662f\u5426\u5927\u4e8e10\nvif_var = []\nfor i in range(6):\n    if df_aux.iloc[i, 2] > 10:\n        vif_var.append(["X" + str(i+1)])\ndf_vif_var = pd.DataFrame(vif_var)\nprint("VIF\u503c\u5927\u4e8e10\u7684\u89e3\u91ca\u53d8\u91cf\u6709\uff1a")\nfor x in df_vif_var[0]:\n    print(x)\n# \u591a\u91cd\u5171\u7ebf\u6027\u8bca\u65ad\u539f\u52194\nprint("\u591a\u91cd\u5171\u7ebf\u6027\u8bca\u65ad\u539f\u52194\uff1aVIF\u503c\u5927\u4e8e10\u65f6\uff0c\u8be5\u89e3\u91ca\u53d8\u91cf\u5b58\u5728\u9ad8\u5ea6\u591a\u91cd\u5171\u7ebf\u6027\u3002")\nprint("\u7ed3\u8bba\uff1a\u4ece\u4e0a\u8ff0\u8f85\u52a9\u56de\u5f52\u7684TOL\u548cVIF\u503c\u6765\u770b\uff0c\u89e3\u91ca\u53d8\u91cfX1\u3001X2\u3001X3\u3001X5\u3001X6\u4e4b\u95f4\u5b58\u5728\u9ad8\u5ea6\u7684\u591a\u91cd\u5171\u7ebf\u6027", "\\n\\n")\n\n# \u5904\u7406\u591a\u91cd\u5171\u7ebf\u6027\n# \u7b80\u5355\u5220\u9664\u6cd5\n# \u5b9a\u4e49\u53d8\u91cf\ny = df.Y\nX1 = df["X1"]\nX2 = df["X2"]\ndf["X2_X1"] = X2\/X1\nx = df[["X2_X1", "X4", "X5"]]\n# \u6dfb\u52a0\u5e38\u6570\u9879\nX = sm.add_constant(x)\n# \u5c55\u793a\u56de\u5f52\u7ed3\u679c\nOLS_model = sm.OLS(y, X).fit()\nprint("\u7ecf\u8fc7\u7b80\u5355\u5220\u9664\u540e\uff0c\u6700\u7ec8\u7684\u56de\u5f52\u7ed3\u679c\u4e3a\uff1a")\nprint(OLS_model.summary(), "\\n")\n\n# \u9010\u6b65\u5220\u9664\u6cd5\n# \u65b9\u6cd5\uff1a\u540e\u5411\u9010\u6b65\u56de\u5f52\uff08\u6240\u6709\u53d8\u91cf\u5bfc\u5165\uff0c\u9010\u6b65\u5220\u9664\u4e0d\u663e\u8457\u7684\u53d8\u91cf\uff09\n# \u5b9a\u4e49\u53d8\u91cf\ny = df.Y\nx = df.iloc[:, 2:8]\n# \u6dfb\u52a0\u5e38\u6570\u9879\nX = sm.add_constant(x)\n# \u5c55\u793a\u6240\u6709\u89e3\u91ca\u53d8\u91cf\nprint("\u5168\u90e8\u7684\u89e3\u91ca\u53d8\u91cf\u4e3a\uff1a")\nprint(X, "\\n")\n# \u5c55\u793a\u521d\u59cb\u56de\u5f52\u7ed3\u679c\nOLS_model = sm.OLS(y, X).fit()\nprint("\u521d\u59cb\u7684\u56de\u5f52\u7ed3\u679c\u4e3a\uff1a")\nprint(OLS_model.summary(), "\\n")\np_values = OLS_model.pvalues\np_max = p_values.max()\n# \u5224\u65adP\u503c-\u5254\u9664\u89e3\u91ca\u53d8\u91cf-\u91cd\u65b0\u56de\u5f52\nwhile p_max > 0.05:                       # \u5faa\u73af\u5f00\u59cb\u7684\u5224\u65ad\u6761\u4ef6\uff0c\u53c2\u6570P\u503c\u662f\u5426\u5927\u4e8e0.05\n    X_num = p_values.argmax()             # \u83b7\u53d6\u6700\u5927P\u503c\u5bf9\u5e94\u7684\u884c\u7d22\u5f15\u53f7\n    X_name = p_values.index[X_num]        # \u83b7\u53d6\u6700\u5927P\u503c\u7684\u7d22\u5f15\u503c\uff0c\u6bd4\u5982\uff1aX5\n    X = X.drop([X_name], axis=1)          # \u5254\u9664\u6700\u5927P\u503c\u5bf9\u5e94\u7684X\u6570\u636e\u5217\uff0c\u6bd4\u5982X5\u5217\n    print("\u5254\u9664\u89e3\u91ca\u53d8\u91cf:" + X_name)         # \u63d0\u793a\u5254\u9664\u53d8\u91cf\n    OLS_model = sm.OLS(y, X).fit()        # \u91cd\u65b0\u56de\u5f52\n    p_values = OLS_model.pvalues          # \u83b7\u53d6\u65b0\u56de\u5f52\u7684\u53c2\u6570P\u503c\n    p_max = p_values.max()                # \u83b7\u53d6\u6700\u5927\u7684\u53c2\u6570P\u503c\nelse:\n    print("\u6240\u6709\u89e3\u91ca\u53d8\u91cf\u5bf9\u5e94\u7684P\u503c\u5747\u5c0f\u4e8e0.05\uff0c\u540e\u5411\u9010\u6b65\u56de\u5f52\u7ed3\u675f\u3002", "\\n")\n    print("\u6700\u7ec8\u7684\u56de\u5f52\u7ed3\u679c\u4e3a\uff1a")\n    print(OLS_model.summary(), "\\n")\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
\u4f8b\u5b50\uff1a \u4ee3\u7801\u90e8\u5206 # lec05 # \u8ba1\u91cf\u5b9e\u9a8c3-\u4ee3\u7801\u90e8\u5206-02 \u591a\u91cd\u5171\u7ebf\u6027\u7684\u8bca\u65ad\u4e0e\u5904\u7406 # \u5bfc\u5165\u5e93 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[29,30],"tags":[],"class_list":["post-5052","post","type-post","status-publish","format-standard","hentry","category-29","category-30"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/seit2019.xyz\/index.php?rest_route=\/wp\/v2\/posts\/5052","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/seit2019.xyz\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/seit2019.xyz\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/seit2019.xyz\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/seit2019.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5052"}],"version-history":[{"count":0,"href":"https:\/\/seit2019.xyz\/index.php?rest_route=\/wp\/v2\/posts\/5052\/revisions"}],"wp:attachment":[{"href":"https:\/\/seit2019.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5052"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/seit2019.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5052"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/seit2019.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5052"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}