{"id":3920,"date":"2023-07-14T18:26:54","date_gmt":"2023-07-14T18:26:54","guid":{"rendered":"https:\/\/statorials.org\/my\/cubic-regression-python\/"},"modified":"2023-07-14T18:26:54","modified_gmt":"2023-07-14T18:26:54","slug":"cubic-regression-python","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/cubic-regression-python\/","title":{"rendered":"Python \u1010\u103d\u1004\u103a\u1000\u102f\u1017\u101c\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u100a\u103a\u1038"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Cubic regression<\/strong> \u101e\u100a\u103a \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038 \u1006\u1000\u103a\u1014\u103d\u103e\u101a\u103a\u1019\u103e\u102f\u1019\u101f\u102f\u1010\u103a\u101e\u1031\u102c\u1021\u1001\u102b\u1010\u103d\u1004\u103a \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1010\u103d\u1000\u103a\u1006\u1011\u102c\u1038\u101e\u1031\u102c\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1014\u103e\u1004\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1000\u103c\u102c\u1038\u101b\u103e\u102d \u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \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\u101e\u1031\u102c \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1021\u1019\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a Python \u1010\u103d\u1004\u103a \u1000\u102f\u1017\u101c\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\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\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">\u1025\u1015\u1019\u102c- Python \u101b\u103e\u102d \u1000\u102f\u1017\u101c\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1010\u103d\u1004\u103a variable \u1014\u103e\u1005\u103a\u1001\u102f (x \u1014\u103e\u1004\u1037\u103a y) \u1015\u102b\u101b\u103e\u102d\u101e\u1031\u102c \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1015\u1014\u103a\u1012\u102b DataFrame \u101b\u103e\u102d\u101e\u100a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">import<\/span> pandas <span style=\"color: #107d3f;\">as<\/span> pd\n\n<span style=\"color: #008080;\">#createDataFrame\n<\/span>df = pd. <span style=\"color: #3366ff;\">DataFrame<\/span> ({' <span style=\"color: #ff0000;\">x<\/span> ': [6, 9, 12, 16, 22, 28, 33, 40, 47, 51, 55, 60],\n                   ' <span style=\"color: #ff0000;\">y<\/span> ': [14, 28, 50, 64, 67, 57, 55, 57, 68, 74, 88, 110]})\n\n<span style=\"color: #008080;\">#view DataFrame\n<\/span><span style=\"color: #008000;\">print<\/span> (df)\n\n     xy\n0 6 14\n1 9 28\n2 12 50\n3 16 64\n4 22 67\n5 28 57\n6 33 55\n7 40 57\n8 47 68\n9 51 74\n10 55 88\n11 60 110\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1024\u1012\u1031\u1010\u102c\u104f \u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101e\u1031\u102c \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1015\u103a\u1016\u103c\u102c\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u1015\u103c\u102f\u101c\u102f\u1015\u103a\u1015\u102b\u1000\u104a \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1014\u103e\u1005\u103a\u1001\u102f\u1000\u103c\u102c\u1038\u101b\u103e\u102d \u1006\u1000\u103a\u1014\u103d\u103e\u101a\u103a\u1019\u103e\u102f\u101e\u100a\u103a \u1019\u103b\u1009\u103a\u1038\u1019\u100a\u102e\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1010\u103d\u1031\u1037\u1019\u103c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">import <span style=\"color: #000000;\">matplotlib. <span style=\"color: #3366ff;\">pyplot<\/span><\/span> as <span style=\"color: #000000;\">plt<\/span>\n\n<span style=\"color: #000000;\"><span style=\"color: #008080;\">#create scatterplot\n<\/span>plt. <span style=\"color: #3366ff;\">scatter<\/span> (df. <span style=\"color: #3366ff;\">x<\/span> , df. <span style=\"color: #3366ff;\">y<\/span> )<\/span><\/span><\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-31513 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/cubique1.jpg\" alt=\"\" width=\"463\" height=\"341\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">x \u104f\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1010\u102d\u102f\u1038\u101c\u102c\u101e\u100a\u103a\u1014\u103e\u1004\u1037\u103a\u1021\u1019\u103b\u103e y \u101e\u100a\u103a \u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1011\u102c\u1038\u101e\u1031\u102c\u1021\u1019\u103e\u1010\u103a\u101e\u102d\u102f\u1037\u1010\u102d\u102f\u1038\u101c\u102c\u1015\u103c\u102e\u1038 \u101c\u103b\u1031\u102c\u1037\u1014\u100a\u103a\u1038\u101e\u103d\u102c\u1038\u101e\u100a\u103a\u104a \u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a \u1011\u1015\u103a\u1010\u102d\u102f\u1038\u101c\u102c\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1000\u103d\u1000\u103a\u1000\u103d\u1000\u103a\u101b\u103e\u102d &#8220; \u1019\u103b\u1009\u103a\u1038\u1000\u103d\u1031\u1038&#8221;  \u1014\u103e\u1005\u103a\u1001\u102f\u1015\u102b\u101e\u1031\u102c \u1024\u1015\u102f\u1036\u1005\u1036\u101e\u100a\u103a \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1014\u103e\u1005\u103a\u1001\u102f\u1000\u103c\u102c\u1038\u101b\u103e\u102d \u1000\u102f\u1017\u102d\u1015\u103a\u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u100a\u103d\u103e\u1014\u103a\u1015\u103c\u1014\u1031\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c cubic regression model \u101e\u100a\u103a variable \u1014\u103e\u1005\u103a\u1001\u102f\u1000\u103c\u102c\u1038\u101b\u103e\u102d \u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f\u1000\u102d\u102f quantify \u101c\u102f\u1015\u103a\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a \u1000\u1031\u102c\u1004\u103a\u1038\u1019\u103d\u1014\u103a\u101e\u1031\u102c \u1000\u102d\u102f\u101a\u103a\u1005\u102c\u1038\u101c\u103e\u101a\u103a\u101c\u1031\u102c\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1000\u102f\u1017\u101c\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1014\u103a\u104a <a href=\"https:\/\/numpy.org\/doc\/stable\/reference\/generated\/numpy.polyfit.html\" target=\"_blank\" rel=\"noopener noreferrer\">numpy.polyfit()<\/a> <span style=\"color: #000000;\">\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1000\u102d\u102f<\/span> \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u1012\u102e\u1002\u101b\u102e 3 \u1015\u102b\u101e\u1031\u102c \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1015\u1019\u102c\u100f \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1016\u103c\u100a\u1037\u103a\u101e\u103d\u1004\u103a\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">import<\/span> numpy <span style=\"color: #107d3f;\">as<\/span> np\n\n<span style=\"color: #008080;\">#fit cubic regression model\n<\/span>model = np. <span style=\"color: #3366ff;\">poly1d<\/span> (np. <span style=\"color: #3366ff;\">polyfit<\/span> (df. <span style=\"color: #3366ff;\">x<\/span> , df. <span style=\"color: #3366ff;\">y<\/span> , <span style=\"color: #000000;\">3))<\/span>\n\n<span style=\"color: #008080;\">#add fitted cubic regression line to scatterplot\n<\/span>polyline = np. <span style=\"color: #3366ff;\">linspace<\/span> (1, 60, 50)\nplt. <span style=\"color: #3366ff;\">scatter<\/span> (df. <span style=\"color: #3366ff;\">x<\/span> , df. <span style=\"color: #3366ff;\">y<\/span> )\nplt. <span style=\"color: #3366ff;\">plot<\/span> (polyline, model(polyline))\n\n<span style=\"color: #008080;\">#add axis labels\n<\/span>plt. <span style=\"color: #3366ff;\">xlabel<\/span> (' <span style=\"color: #ff0000;\">x<\/span> ')\nplt. <span style=\"color: #3366ff;\">ylabel<\/span> (' <span style=\"color: #ff0000;\">y<\/span> ')\n\n<span style=\"color: #008080;\">#displayplot\n<\/span>plt. <span style=\"color: #3366ff;\">show<\/span> ()<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-31514\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/cubique2.jpg\" alt=\"Python \u1010\u103d\u1004\u103a\u1000\u102f\u1017\u101c\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\" width=\"547\" height=\"404\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">\u1019\u1031\u102c\u103a\u1012\u101a\u103a coefficients \u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101b\u102d\u102f\u1000\u103a\u1014\u103e\u102d\u1015\u103a\u1001\u103c\u1004\u103a\u1038\u1016\u103c\u1004\u1037\u103a \u1010\u1015\u103a\u1006\u1004\u103a\u1011\u102c\u1038\u101e\u1031\u102c \u1000\u102f\u1017\u1006\u102f\u1010\u103a\u1006\u102f\u1010\u103a\u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u101b\u101a\u1030\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">print<\/span> (model)\n\n          3 2\n0.003302x - 0.3214x + 9.832x - 32.01\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1010\u1015\u103a\u1006\u1004\u103a\u1011\u102c\u1038\u101e\u1031\u102c \u1000\u102f\u1017\u1006\u102f\u1010\u103a\u1006\u102f\u1010\u103a\u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u1019\u103e\u102c-<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>y = 0.003302(x) <sup>3<\/sup> \u2013 0.3214(x) <sup>2<\/sup> + 9.832x \u2013 30.01<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">x \u104f\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1021\u1015\u1031\u102b\u103a\u1021\u1001\u103c\u1031\u1001\u1036\u104d y \u104f\u1019\u103b\u103e\u1031\u102c\u103a\u1019\u103e\u1014\u103a\u1038\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f\u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u1024\u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u1000\u102d\u102f\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;\">\u1025\u1015\u1019\u102c\u104a x \u101e\u100a\u103a 30 \u1016\u103c\u1005\u103a\u1015\u102b\u1000\u104a y \u1021\u1010\u103d\u1000\u103a \u1019\u103b\u103e\u1031\u102c\u103a\u1019\u103e\u1014\u103a\u1038\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103e\u102c 64.844 \u1016\u103c\u1005\u103a\u101e\u100a\u103a \u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">y = 0.003302(30) <sup>3<\/sup> \u2013 0.3214(30) <sup>2<\/sup> + 9.832(30) \u2013 30.01 = 64.844<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1019\u1031\u102c\u103a\u1012\u101a\u103a\u104f R-squared \u1000\u102d\u102f\u101b\u101b\u1014\u103a \u1021\u1010\u102d\u102f\u1001\u103b\u102f\u1036\u1038\u101b\u1031\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104a \u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u101b\u103e\u102d \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u104f\u1021\u1001\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define function to calculate r-squared<\/span>\n<span style=\"color: #008000;\">def<\/span> polyfit(x, y, degree):\n    results = {}\n    coeffs = np. <span style=\"color: #3366ff;\">polyfit<\/span> (x, y, degree)\n    p = np. <span style=\"color: #3366ff;\">poly1d<\/span> (coeffs)\n    <span style=\"color: #008080;\">#calculate r-squared<\/span>\n    yhat = p(x)\n    ybar = np. <span style=\"color: #3366ff;\">sum<\/span> (y)\/len(y)\n    ssreg = np. <span style=\"color: #3366ff;\">sum<\/span> ((yhat-ybar) <span style=\"color: #800080;\">**<\/span> 2)\n    sstot = np. <span style=\"color: #3366ff;\">sum<\/span> ((y - ybar) <span style=\"color: #800080;\">**<\/span> 2)\n    results[' <span style=\"color: #ff0000;\">r_squared<\/span> '] = ssreg \/ sstot\n\n    <span style=\"color: #008000;\">return<\/span> results\n\n<span style=\"color: #008080;\">#find r-squared of polynomial model with degree = 3\n<\/span>polyfit(df. <span style=\"color: #3366ff;\">x<\/span> , df. <span style=\"color: #3366ff;\">y<\/span> , 3)\n\n{'r_squared': 0.9632469890057967}\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1024\u1025\u1015\u1019\u102c\u1010\u103d\u1004\u103a\u104a \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u104f R \u1005\u1010\u102f\u101b\u1014\u103a\u1038\u101e\u100a\u103a <strong>0.9632<\/strong> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1010\u103d\u1004\u103a \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f 96.32% \u1000\u102d\u102f \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1000 \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u101e\u100a\u103a \u1021\u101c\u103d\u1014\u103a\u1019\u103c\u1004\u1037\u103a\u1019\u102c\u1038\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a \u1000\u102f\u1017\u101c\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u101e\u100a\u103a \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1014\u103e\u1005\u103a\u1001\u102f\u1000\u103c\u102c\u1038\u101b\u103e\u102d \u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1000\u1031\u102c\u1004\u103a\u1038\u1019\u103d\u1014\u103a\u1005\u103d\u102c \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1015\u1031\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u104e\u1004\u103a\u1038\u1000\u1006\u102d\u102f\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1006\u1000\u103a\u1005\u1015\u103a\u1019\u103e\u102f-<\/strong> <a href=\"https:\/\/statorials.org\/my\/r-\u1014\u103e\u1005\u103a\u1011\u1015\u103a\u1000\u102d\u1014\u103a\u1038\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u1031\u102c\u1004\u103a\u1038\u101e\u100a\u103a\u104b\/\" target=\"_blank\" rel=\"noopener\">\u1000\u1031\u102c\u1004\u103a\u1038\u101e\u1031\u102c R-squared \u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1006\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c \u1021\u1018\u101a\u103a\u1014\u100a\u103a\u1038\u104b<\/a><\/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 \u1021\u101e\u102f\u1036\u1038\u1019\u103b\u102c\u1038\u101e\u1031\u102c \u1021\u101c\u102f\u1015\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> <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\">Python \u1010\u103d\u1004\u103a \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\/quadratic-regression-python\/\" target=\"_blank\" rel=\"noopener\">Python \u1010\u103d\u1004\u103a quadratic 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 noreferrer\">Python \u1010\u103d\u1004\u103a polynomial regression \u101c\u102f\u1015\u103a\u1014\u100a\u103a\u1038<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Cubic regression \u101e\u100a\u103a \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038 \u1006\u1000\u103a\u1014\u103d\u103e\u101a\u103a\u1019\u103e\u102f\u1019\u101f\u102f\u1010\u103a\u101e\u1031\u102c\u1021\u1001\u102b\u1010\u103d\u1004\u103a \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1010\u103d\u1000\u103a\u1006\u1011\u102c\u1038\u101e\u1031\u102c\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1014\u103e\u1004\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1000\u103c\u102c\u1038\u101b\u103e\u102d \u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \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\u101e\u1031\u102c \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1021\u1019\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a Python \u1010\u103d\u1004\u103a \u1000\u102f\u1017\u101c\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\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\u1011\u102c\u1038\u101e\u100a\u103a\u104b \u1025\u1015\u1019\u102c- Python \u101b\u103e\u102d \u1000\u102f\u1017\u101c\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1010\u103d\u1004\u103a variable \u1014\u103e\u1005\u103a\u1001\u102f (x \u1014\u103e\u1004\u1037\u103a y) \u1015\u102b\u101b\u103e\u102d\u101e\u1031\u102c \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1015\u1014\u103a\u1012\u102b DataFrame \u101b\u103e\u102d\u101e\u100a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b import pandas as pd #createDataFrame df = pd. DataFrame ({&#8216; x &#8216;: [6, 9, 12, 16, 22, 28, 33, 40, 47, 51, 55, 60], [&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 - Statorials \u1010\u103d\u1004\u103a\u1000\u102f\u1017\u101c\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u100a\u103a\u1038<\/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 \u1000\u102f\u1017\u101c\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1000\u102d\u102f 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content=\"\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a Python \u1010\u103d\u1004\u103a \u1000\u102f\u1017\u101c\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\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 \u1025\u1015\u1019\u102c\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1004\u1037\u103a \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/my\/cubic-regression-python\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-14T18:26:54+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/cubique1.jpg\" \/>\n<meta name=\"author\" content=\"Benjamin Anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin Anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/my\/cubic-regression-python\/\",\"url\":\"https:\/\/statorials.org\/my\/cubic-regression-python\/\",\"name\":\"Python - Statorials 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