{"id":882,"date":"2023-07-28T10:44:58","date_gmt":"2023-07-28T10:44:58","guid":{"rendered":"https:\/\/statorials.org\/my\/polynomial-regression-%e1%80%85%e1%80%95%e1%80%ab%e1%80%b8%e1%80%a1%e1%80%af%e1%80%b6%e1%80%b8\/"},"modified":"2023-07-28T10:44:58","modified_gmt":"2023-07-28T10:44:58","slug":"polynomial-regression-%e1%80%85%e1%80%95%e1%80%ab%e1%80%b8%e1%80%a1%e1%80%af%e1%80%b6%e1%80%b8","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/polynomial-regression-%e1%80%85%e1%80%95%e1%80%ab%e1%80%b8%e1%80%a1%e1%80%af%e1%80%b6%e1%80%b8\/","title":{"rendered":"Python \u1010\u103d\u1004\u103a polynomial regression \u101c\u102f\u1015\u103a\u1014\u100a\u103a\u1038"},"content":{"rendered":"

<\/p>\n

\n

\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1001\u103c\u1004\u103a\u1038\u1000\u102d\u102f \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 \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1010\u102d\u102f\u1037\u1000\u103c\u102c\u1038 \u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b<\/span><\/p>\n

\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1019\u103e\u102f\u104f \u1021\u101e\u102f\u1036\u1038\u1021\u1019\u103b\u102c\u1038\u1006\u102f\u1036\u1038\u1021\u1019\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038\u1019\u103e\u102c \u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101e\u1031\u102c\u1019\u103b\u1009\u103a\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f<\/a> \u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038\u104a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1014\u103e\u1004\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u101e\u100a\u103a \u1019\u103b\u1009\u103a\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1006\u1000\u103a\u1005\u1015\u103a\u1019\u103e\u102f\u101b\u103e\u102d\u101e\u100a\u1037\u103a\u1021\u1001\u102b \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b<\/span> <\/p>\n

\"\"<\/p>\n

\u101e\u102d\u102f\u1037\u101e\u1031\u102c\u103a \u1010\u1005\u103a\u1001\u102b\u1010\u1005\u103a\u101b\u1036\u1010\u103d\u1004\u103a \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\u1014\u103e\u1004\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1000\u103c\u102c\u1038 \u1006\u1000\u103a\u1006\u1036\u101b\u1031\u1038\u101e\u100a\u103a \u101c\u102d\u102f\u1004\u103a\u1038\u1019\u101f\u102f\u1010\u103a\u1015\u1031\u104b<\/span><\/p>\n

\u1025\u1015\u1019\u102c\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u1005\u1005\u103a\u1019\u103e\u1014\u103a\u101e\u1031\u102c\u1006\u1000\u103a\u1006\u1036\u101b\u1031\u1038\u101e\u100a\u103a \u101c\u1031\u1038\u1011\u1031\u102c\u1004\u1037\u103a\u1015\u102f\u1036\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span> <\/p>\n

\"\"<\/p>\n

\u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1000\u102f\u1017\u102d\u101c\u103a\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span> <\/p>\n

\"\"<\/p>\n

\u1024\u1000\u102d\u1005\u1039\u1005\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a\u104a \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038\u1010\u103d\u1004\u103a linear \u1019\u101f\u102f\u1010\u103a\u101e\u1031\u102c \u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u1037\u103a polynomial regression<\/strong> \u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u103c\u1004\u103a\u1038\u101e\u100a\u103a \u1021\u1013\u102d\u1015\u1039\u1015\u102b\u101a\u103a\u101b\u103e\u102d\u1005\u1031\u101e\u100a\u103a\u104b<\/span><\/p>\n

\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a Python \u1010\u103d\u1004\u103a polynomial regression \u101c\u102f\u1015\u103a\u1014\u100a\u103a\u1038\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n

\u1025\u1015\u1019\u102c- Python \u101b\u103e\u102d Polynomial Regression<\/strong><\/span><\/h2>\n

Python \u1010\u103d\u1004\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a (x) \u1014\u103e\u1004\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a (y) \u101b\u103e\u102d\u101e\u100a\u103a \u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b<\/span><\/p>\n

 x = [2, 3, 4, 5, 6, 7, 7, 8, 9, 11, 12]\ny = [18, 16, 15, 17, 20, 23, 25, 28, 31, 30, 29]\n<\/strong><\/pre>\n
 \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 \u1016\u1014\u103a\u1010\u102e\u1038\u1015\u102b\u1000\u104a x \u1014\u103e\u1004\u1037\u103a y \u1021\u1000\u103c\u102c\u1038 \u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f\u1019\u103e\u102c linear \u1019\u101f\u102f\u1010\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u101b\u103e\u1004\u103a\u1038\u101b\u103e\u1004\u103a\u1038\u101c\u1004\u103a\u1038\u101c\u1004\u103a\u1038 \u101e\u102d\u1019\u103c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span> <\/p>\n
 import<\/span> matplotlib.pyplot as<\/span> plt\n\n#create scatterplot<\/span> \nplt.scatter(x, y)\n<\/strong><\/pre>\n
\"\"<\/p>\n
 import<\/span> numpy as<\/span> np\n\n#polynomial fit with degree = 3\n<\/span>model = np.poly1d(np.polyfit(x, y, 3))\n\n#add fitted polynomial line to scatterplot\n<\/span>polyline = np.linspace(1, 12, 50)\nplt.scatter(x, y)\nplt.plot(polyline, model(polyline))\nplt.show()<\/strong> <\/pre>\n
\"Python<\/p>\n
 \u1019\u1031\u102c\u103a\u1012\u101a\u103a coefficients \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 polynomial regression equation \u1000\u102d\u102f \u101b\u101a\u1030\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n
 print(model)\n\npoly1d([ -0.10889554, 2.25592957, -11.83877127, 33.62640038])\n<\/strong><\/pre>\n
 \u1010\u1015\u103a\u1006\u1004\u103a\u1011\u102c\u1038\u101e\u1031\u102c polynomial \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u1019\u103e\u102c-<\/span><\/p>\n
 y = -0.109x 3<\/sup> + 2.256x 2<\/sup> \u2013 11.839x + 33.626<\/strong><\/span><\/p>\n
 \u1024\u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u1021\u102c\u1038 \u101b\u103e\u1004\u103a\u1038\u101c\u1004\u103a\u1038\u1001\u103b\u1000\u103a\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u104f \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1010\u1005\u103a\u1001\u102f\u1015\u1031\u1038\u1011\u102c\u1038\u101e\u100a\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u104f\u1019\u103b\u103e\u1031\u102c\u103a\u1019\u103e\u1014\u103a\u1038\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u101b\u103e\u102c\u1016\u103d\u1031\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n
 \u1025\u1015\u1019\u102c\u104a x = 4 \u101f\u102f\u101a\u1030\u1006\u1015\u102b\u104b \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\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 y \u1016\u103c\u1005\u103a\u101c\u102d\u1019\u1037\u103a\u1019\u100a\u103a-<\/span><\/p>\n
 y = -0.109(4) 3<\/sup> + 2.256(4) 2<\/sup> \u2013 11.839(4) + 33.626= 15.39<\/b> \u104b<\/span><\/p>\n
 \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
 #define function to calculate r-squared<\/span>\ndef<\/span> polyfit(x, y, degree):\n    results = {}\n    coeffs = numpy.polyfit(x, y, degree)\n    p = numpy.poly1d(coeffs)\n    #calculate r-squared<\/span>\n    yhat = p(x)\n    ybar = numpy.sum(y)\/len(y)\n    ssreg = numpy.sum((yhat-ybar)**2)\n    sstot = numpy.sum((y - ybar)**2)\n    results['r_squared'] = ssreg \/ sstot\n\n    return<\/span> results\n\n#find r-squared of polynomial model with degree = 3\n<\/span>polyfit(x, y, 3)\n\n{'r_squared': 0.9841113454245183}\n<\/strong><\/pre>\n
 \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 0.9841<\/strong> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n
 \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\u104f 98.41%<\/strong> \u101e\u100a\u103a \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\u1019\u103b\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"
\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1001\u103c\u1004\u103a\u1038\u1000\u102d\u102f \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 \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1010\u102d\u102f\u1037\u1000\u103c\u102c\u1038 \u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1019\u103e\u102f\u104f \u1021\u101e\u102f\u1036\u1038\u1021\u1019\u103b\u102c\u1038\u1006\u102f\u1036\u1038\u1021\u1019\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038\u1019\u103e\u102c \u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101e\u1031\u102c\u1019\u103b\u1009\u103a\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f \u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038\u104a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1014\u103e\u1004\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u101e\u100a\u103a 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 \u1011\u102d\u102f\u1037\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1024\u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1000\u103a linear regression model \u1000\u102d\u102f \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u101b\u1014\u103a \u1021\u1013\u102d\u1015\u1039\u1015\u102b\u101a\u103a\u1019\u101b\u103e\u102d\u1015\u1031\u104b \u101a\u1004\u103a\u1038\u1021\u1005\u102c\u1038\u104a numpy.polyfit()<\/a> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u1012\u102e\u1002\u101b\u102e 3 \u1014\u103e\u1004\u1037\u103a polynomial \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1000\u102d\u102f \u1021\u1036\u101d\u1004\u103a\u1001\u103d\u1004\u103a\u1000\u103b\u1016\u103c\u1005\u103a\u1021\u1031\u102c\u1004\u103a \u1000\u103c\u102d\u102f\u1038\u1015\u1019\u103a\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span> <\/p>\n