{"id":4505,"date":"2023-07-10T14:11:32","date_gmt":"2023-07-10T14:11:32","guid":{"rendered":"https:\/\/statorials.org\/my\/wald-%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba-python\/"},"modified":"2023-07-10T14:11:32","modified_gmt":"2023-07-10T14:11:32","slug":"wald-%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba-python","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/wald-%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba-python\/","title":{"rendered":"Python \u1010\u103d\u1004\u103a wald test \u1015\u103c\u102f\u101c\u102f\u1015\u103a\u1014\u100a\u103a\u1038"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1010\u1005\u103a\u1001\u102f \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1010\u1005\u103a\u1001\u102f\u1011\u1000\u103a\u1015\u102d\u102f\u101e\u1031\u102c \u1018\u1031\u102c\u1004\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1010\u1030\u100a\u102e\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a <strong>Wald \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f<\/strong> \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1010\u103d\u1004\u103a \u1010\u1005\u103a\u1001\u102f \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1010\u1005\u103a\u1001\u102f\u1011\u1000\u103a\u1015\u102d\u102f\u101e\u1031\u102c \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101e\u102f\u100a\u1014\u103e\u1004\u1037\u103a \u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u1024\u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u1000\u103c\u102c\u1001\u100f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u1021\u1010\u103d\u1000\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b null \u1014\u103e\u1004\u1037\u103a \u1021\u1001\u103c\u102c\u1038\u1021\u1001\u103c\u102c\u1038\u101e\u1031\u102c <a href=\"https:\/\/statorials.org\/my\/\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103c\u1004\u103a\u1038-\u1041\/\" target=\"_blank\" rel=\"noopener\">\u1021\u101a\u1030\u1021\u1006\u1019\u103b\u102c\u1038\u1000\u102d\u102f<\/a> \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a-<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub><\/strong> : \u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1021\u1010\u103d\u1032\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101e\u102f\u100a\u1014\u103e\u1004\u1037\u103a\u100a\u102e\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>H <sub>A<\/sub><\/strong> : \u1021\u1005\u102f\u101b\u103e\u102d \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1021\u102c\u1038\u101c\u102f\u1036\u1038\u101e\u100a\u103a \u101e\u102f\u100a\u1014\u103e\u1004\u1037\u103a \u100a\u102e\u1019\u103b\u103e\u101e\u100a\u103a\u1019\u101f\u102f\u1010\u103a\u1015\u102b\u104b<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1021\u1000\u101a\u103a\u104d \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1006\u102d\u102f\u101b\u1014\u103a \u1015\u103b\u1000\u103a\u1000\u103d\u1000\u103a\u1015\u102b\u1000\u104a \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1005\u1036\u1015\u103c\u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1019\u103e\u102f\u1010\u103d\u1004\u103a \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c \u1010\u102d\u102f\u1038\u1010\u1000\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u1015\u1036\u1037\u1015\u102d\u102f\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1019\u103e \u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1011\u102c\u1038\u101e\u1031\u102c \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1016\u101a\u103a\u101b\u103e\u102c\u1038\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1025\u1015\u1019\u102c\u101e\u100a\u103a Python \u1010\u103d\u1004\u103a Wald \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1014\u100a\u103a\u1038\u1000\u102d\u102f\u1015\u103c\u101e\u101e\u100a\u103a\u104b<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u1025\u1015\u1019\u102c- Python \u1010\u103d\u1004\u103a Wald \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u1024\u1025\u1015\u1019\u102c\u1021\u1010\u103d\u1000\u103a\u104a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1019\u103b\u102c\u1038\u1005\u103d\u102c\u101e\u1031\u102c linear regression model \u1014\u103e\u1004\u1037\u103a\u1000\u102d\u102f\u1000\u103a\u100a\u102e\u101b\u1014\u103a \u1014\u102c\u1019\u100a\u103a\u1000\u103c\u102e\u1038 <strong>mtcars<\/strong> dataset \u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">mpg = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub> \u101b\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a + \u03b2 <sub>2<\/sub> carb + \u03b2 <sub>3<\/sub> hp + \u03b2 <sub>4<\/sub> cyl<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u102f\u1012\u103a\u101e\u100a\u103a \u1024\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1014\u103e\u1004\u1037\u103a \u1021\u1036\u101d\u1004\u103a\u1001\u103d\u1004\u103a\u1000\u103b\u1016\u103c\u1005\u103a\u1015\u102f\u1036\u1000\u102d\u102f \u1015\u103c\u101e\u1015\u103c\u102e\u1038 \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1021\u1000\u103b\u1009\u103a\u1038\u1001\u103b\u102f\u1015\u103a\u1000\u102d\u102f \u1015\u103c\u101e\u101e\u100a\u103a-<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">import<\/span> statsmodels. <span style=\"color: #3366ff;\">formula<\/span> . <span style=\"color: #3366ff;\">api<\/span> <span style=\"color: #008000;\">as<\/span> smf\n<span style=\"color: #008000;\">import<\/span> pandas <span style=\"color: #008000;\">as<\/span> pd\n<span style=\"color: #008000;\">import<\/span> io\n\n<span style=\"color: #008080;\">#define dataset as string\n<\/span>mtcars_data=\"\"\"model,mpg,cyl,disp,hp,drat,wt,qsec,vs,am,gear,carb\nMazda RX4,21,6,160,110,3.9,2.62,16.46,0,1,4,4\nMazda RX4 Wag,21.6,160,110,3.9,2.875,17.02,0,1,4,4\nDatsun 710,22.8,4,108,93,3.85,2.32,18.61,1,1,4,1\nHornet 4 Drive,21.4,6,258,110,3.08,3.215,19.44,1,0,3,1\nHornet Sportabout,18.7,8,360,175,3.15,3.44,17.02,0,0,3,2\nValiant,18.1,6,225,105,2.76,3.46,20.22,1,0,3,1\nDuster 360,14.3,8,360,245,3.21,3.57,15.84,0,0,3,4\nMerc 240D,24.4,4,146.7,62,3.69,3.19,20,1,0,4,2\nMerc 230,22.8,4,140.8,95,3.92,3.15,22.9,1,0,4,2\nMerc 280,19.2,6,167.6,123,3.92,3.44,18.3,1,0,4,4\nMerc 280C,17.8,6,167.6,123,3.92,3.44,18.9,1,0,4,4\nMerc 450SE,16.4,8,275.8,180,3.07,4.07,17.4,0,0,3,3\nMerc 450SL,17.3,8,275.8,180,3.07,3.73,17.6,0,0,3,3\nMerc 450SLC,15.2,8,275.8,180,3.07,3.78,18,0,0,3,3\nCadillac Fleetwood,10.4,8,472,205,2.93,5.25,17.98,0,0,3,4\nLincoln Continental,10.4,8,460,215,3,5.424,17.82,0,0,3,4\nChrysler Imperial,14.7,8,440,230,3.23,5.345,17.42,0,0,3,4\nFiat 128,32.4,4,78.7,66,4.08,2.2,19.47,1,1,4,1\nHonda Civic,30.4,4,75.7,52,4.93,1.615,18.52,1,1,4,2\nToyota Corolla,33.9,4,71.1,65,4.22,1.835,19.9,1,1,4,1\nToyota Corona,21.5,4,120.1,97,3.7,2.465,20.01,1,0,3,1\nDodge Challenger,15.5,8,318,150,2.76,3.52,16.87,0,0,3,2\nAMC Javelin,15.2,8,304,150,3.15,3.435,17.3,0,0,3,2\nCamaro Z28,13.3,8,350,245,3.73,3.84,15.41,0,0,3,4\nPontiac Firebird,19.2,8,400,175,3.08,3.845,17.05,0,0,3,2\nFiat X1-9,27.3,4,79,66,4.08,1.935,18.9,1,1,4,1\nPorsche 914-2,26,4,120.3,91,4.43,2.14,16.7,0,1,5,2\nLotus Europa,30.4,4,95.1,113,3.77,1.513,16.9,1,1,5,2\nFord Pantera L,15.8,8,351,264,4.22,3.17,14.5,0,1,5,4\nFerrari Dino,19.7,6,145,175,3.62,2.77,15.5,0,1,5,6\nMaserati Bora,15.8,301,335,3.54,3.57,14.6,0,1,5,8\nVolvo 142E,21.4,4,121,109,4.11,2.78,18.6,1,1,4,2\"\"\"\n\n<span style=\"color: #008080;\">#convert string to DataFrame\n<\/span>df = pd. <span style=\"color: #3366ff;\">read_csv<\/span> ( <span style=\"color: #3366ff;\">io.StringIO<\/span> (mtcars_data), sep=\" <span style=\"color: #ff0000;\">,<\/span> \")\n\n<span style=\"color: #008080;\">#fit multiple linear regression model\n<\/span>results = smf. <span style=\"color: #3366ff;\">ols<\/span> (' <span style=\"color: #ff0000;\">mpg~disp+carb+hp+cyl<\/span> ',df). <span style=\"color: #3366ff;\">fit<\/span> ()\n\n<span style=\"color: #008080;\">#view regression model summary\n<\/span>results. <span style=\"color: #3366ff;\">summary<\/span> ()\n\n\tcoef std err t P&gt;|t| [0.025 0.975]\nIntercept34.0216 2.523 13.482 0.000 28.844 39.199\navailable -0.0269 0.011 -2.379 0.025 -0.050 -0.004\ncarb -0.9269 0.579 -1.601 0.121 -2.115 0.261\nhp 0.0093 0.021 0.452 0.655 -0.033 0.052\ncyl -1.0485 0.784 -1.338 0.192 -2.657 0.560\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a\u104a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a &#8220; hp&#8221;  \u1014\u103e\u1004\u1037\u103a &#8220; cyl&#8221;  \u1014\u103e\u1005\u103a\u1001\u102f\u101c\u102f\u1036\u1038\u1021\u1010\u103d\u1000\u103a \u101e\u102f\u100a\u1014\u103e\u1004\u1037\u103a\u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u101b\u1014\u103a <strong>statsmodels<\/strong> <strong>wald_test()<\/strong> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u102f\u1012\u103a\u101e\u100a\u103a \u1024\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u101c\u1000\u103a\u1010\u103d\u1031\u1037\u1010\u103d\u1004\u103a \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u1015\u103c\u101e\u101e\u100a\u103a-<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#perform Wald Test to determine if 'hp' and 'cyl' coefficients are both zero<\/span>\n<span style=\"color: #008000;\">print<\/span> ( <span style=\"color: #3366ff;\">results.wald_test<\/span> (' <span style=\"color: #ff0000;\">(hp=0, cyl=0)<\/span> '))\n\nF test: F=array([[0.91125429]]), p=0.41403001184235005, df_denom=27, df_num=2\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u101b\u101c\u1012\u103a\u1019\u103e\u104a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f <a href=\"https:\/\/statorials.org\/my\/p-\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u101e\u100a\u103a-\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c-\u1021\u101b\u1031\u1038\u1015\u102b\u1019\u103e\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b\/\" target=\"_blank\" rel=\"noopener\">p-value<\/a> \u101e\u100a\u103a <strong>0.414<\/strong> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1010\u103d\u1031\u1037\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024 p-value \u101e\u100a\u103a 0.05 \u1011\u1000\u103a\u1019\u1014\u100a\u103a\u1038\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a Wald test \u104f null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u101b\u1014\u103a \u1015\u103b\u1000\u103a\u1000\u103d\u1000\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a &#8220; hp&#8221;  \u1014\u103e\u1004\u1037\u103a &#8220; cyl&#8221;  \u1021\u1010\u103d\u1000\u103a \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101e\u102f\u100a\u1014\u103e\u1004\u1037\u103a \u100a\u102e\u1019\u103b\u103e\u101e\u100a\u103a\u101f\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u101a\u1030\u1006\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1021\u101b \u1021\u101c\u102f\u1036\u1038\u1005\u102f\u1036\u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1019\u103e\u102f\u1000\u102d\u102f \u101e\u102d\u101e\u102d\u101e\u102c\u101e\u102c \u1019\u1010\u102d\u102f\u1038\u1010\u1000\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1024\u1005\u100a\u103a\u1038\u1000\u1019\u103a\u1038\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1019\u103e \u1016\u101a\u103a\u101b\u103e\u102c\u1038\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u1011\u1015\u103a\u101c\u1031\u102c\u1004\u103a\u1038\u1021\u101b\u1004\u103a\u1038\u1021\u1019\u103c\u1005\u103a\u1019\u103b\u102c\u1038<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1015\u102b \u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1019\u103b\u102c\u1038\u101e\u100a\u103a Python \u1010\u103d\u1004\u103a \u1021\u1001\u103c\u102c\u1038\u101e\u1031\u102c \u1018\u102f\u1036\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/my\/python-\u1010\u103d\u1004\u103a-\u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101e\u1031\u102c-linear-regression\/\" target=\"_blank\" rel=\"noopener\">\u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101e\u1031\u102c linear regression \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u100a\u103a\u1038<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/polynomial-regression-\u1005\u1015\u102b\u1038\u1021\u102f\u1036\u1038\/\" target=\"_blank\" rel=\"noopener\">Python \u1010\u103d\u1004\u103a polynomial regression \u101c\u102f\u1015\u103a\u1014\u100a\u103a\u1038<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/python-\u1010\u103d\u1004\u103a-vive-\u1010\u103d\u1000\u103a\u1014\u100a\u103a\u1038\/\" target=\"_blank\" rel=\"noopener\">Python \u1010\u103d\u1004\u103a VIF \u1010\u103d\u1000\u103a\u1014\u100a\u103a\u1038<\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1010\u1005\u103a\u1001\u102f \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1010\u1005\u103a\u1001\u102f\u1011\u1000\u103a\u1015\u102d\u102f\u101e\u1031\u102c \u1018\u1031\u102c\u1004\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1010\u1030\u100a\u102e\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a Wald \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1010\u103d\u1004\u103a \u1010\u1005\u103a\u1001\u102f \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1010\u1005\u103a\u1001\u102f\u1011\u1000\u103a\u1015\u102d\u102f\u101e\u1031\u102c \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101e\u102f\u100a\u1014\u103e\u1004\u1037\u103a \u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u1024\u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u1000\u103c\u102c\u1001\u100f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b \u1024\u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u1021\u1010\u103d\u1000\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b null \u1014\u103e\u1004\u1037\u103a \u1021\u1001\u103c\u102c\u1038\u1021\u1001\u103c\u102c\u1038\u101e\u1031\u102c \u1021\u101a\u1030\u1021\u1006\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a- H 0 : \u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1021\u1010\u103d\u1032\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101e\u102f\u100a\u1014\u103e\u1004\u1037\u103a\u100a\u102e\u101e\u100a\u103a\u104b H A : \u1021\u1005\u102f\u101b\u103e\u102d \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1021\u102c\u1038\u101c\u102f\u1036\u1038\u101e\u100a\u103a \u101e\u102f\u100a\u1014\u103e\u1004\u1037\u103a \u100a\u102e\u1019\u103b\u103e\u101e\u100a\u103a\u1019\u101f\u102f\u1010\u103a\u1015\u102b\u104b \u1021\u1000\u101a\u103a\u104d \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1006\u102d\u102f\u101b\u1014\u103a \u1015\u103b\u1000\u103a\u1000\u103d\u1000\u103a\u1015\u102b\u1000\u104a \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1005\u1036\u1015\u103c\u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1019\u103e\u102f\u1010\u103d\u1004\u103a \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c \u1010\u102d\u102f\u1038\u1010\u1000\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u1015\u1036\u1037\u1015\u102d\u102f\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1019\u103e [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Python - Statology \u1010\u103d\u1004\u103a Wald Test \u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1014\u100a\u103a\u1038\u104b<\/title>\n<meta name=\"description\" content=\"\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a Python \u1010\u103d\u1004\u103a Wald \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1014\u100a\u103a\u1038\u1000\u102d\u102f \u1021\u1015\u103c\u100a\u1037\u103a\u1021\u1005\u102f\u1036 \u1025\u1015\u1019\u102c\u1010\u1005\u103a\u1001\u102f\u1021\u1015\u102b\u1021\u101d\u1004\u103a 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