{"id":4060,"date":"2023-07-13T21:08:59","date_gmt":"2023-07-13T21:08:59","guid":{"rendered":"https:\/\/statorials.org\/hi\/%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6-%e0%a4%aa%e0%a5%8d%e0%a4%b0%e0%a4%a4%e0%a4%bf%e0%a4%97%e0%a4%ae%e0%a4%a8-%e0%a4%b8%e0%a5%8d%e0%a4%95%e0%a5%87%e0%a4%b2%e0%a5%87%e0%a4%b0\/"},"modified":"2023-07-13T21:08:59","modified_gmt":"2023-07-13T21:08:59","slug":"%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6-%e0%a4%aa%e0%a5%8d%e0%a4%b0%e0%a4%a4%e0%a4%bf%e0%a4%97%e0%a4%ae%e0%a4%a8-%e0%a4%b8%e0%a5%8d%e0%a4%95%e0%a5%87%e0%a4%b2%e0%a5%87%e0%a4%b0","status":"publish","type":"post","link":"https:\/\/statorials.org\/hi\/%e0%a4%ac%e0%a4%b9%e0%a5%81%e0%a4%aa%e0%a4%a6-%e0%a4%aa%e0%a5%8d%e0%a4%b0%e0%a4%a4%e0%a4%bf%e0%a4%97%e0%a4%ae%e0%a4%a8-%e0%a4%b8%e0%a5%8d%e0%a4%95%e0%a5%87%e0%a4%b2%e0%a5%87%e0%a4%b0\/","title":{"rendered":"\u0938\u094d\u0915\u093f\u0915\u093f\u091f-\u0932\u0930\u094d\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902"},"content":{"rendered":"

<\/p>\n

\n

\u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928<\/a> \u090f\u0915 \u0910\u0938\u0940 \u0924\u0915\u0928\u0940\u0915 \u0939\u0948 \u091c\u093f\u0938\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0939\u092e \u0924\u092c \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u091c\u092c \u090f\u0915 \u092a\u0942\u0930\u094d\u0935\u0938\u0942\u091a\u0915 \u091a\u0930 \u0914\u0930 \u090f\u0915 \u092a\u094d\u0930\u0924\u093f\u0915\u094d\u0930\u093f\u092f\u093e \u091a\u0930<\/a> \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927 \u0905\u0930\u0947\u0916\u0940\u092f \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n

\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u0928\u093f\u092e\u094d\u0928 \u0930\u0942\u092a \u0932\u0947\u0924\u093e \u0939\u0948:<\/span><\/p>\n

\u0935\u093e\u0908 = \u03b2 0<\/sub> +<\/sup> \u03b2 1<\/sub> \u090f\u0915\u094d\u0938 + \u03b2 2<\/sub> \u090f\u0915\u094d\u0938 2<\/sup> + \u2026 + \u03b2 \u090f\u091a<\/sub><\/span><\/p>\n

\u091c\u0939\u093e\u0901 h<\/em> \u092c\u0939\u0941\u092a\u0926 \u0915\u0940 “\u0921\u093f\u0917\u094d\u0930\u0940” \u0939\u0948\u0964<\/span><\/p>\n

\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u091a\u0930\u0923-\u0926\u0930-\u091a\u0930\u0923 \u0909\u0926\u093e\u0939\u0930\u0923 \u0926\u093f\u0916\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0938\u094d\u0915\u0947\u0932\u0947\u0930\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u092a\u093e\u092f\u0925\u0928 \u092e\u0947\u0902 \u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902\u0964<\/span><\/p>\n

\u091a\u0930\u0923 1: \u0921\u0947\u091f\u093e \u092c\u0928\u093e\u090f\u0902<\/strong><\/span><\/h2>\n

\u0938\u092c\u0938\u0947 \u092a\u0939\u0932\u0947, \u0906\u0907\u090f \u090f\u0915 \u092d\u0935\u093f\u0937\u094d\u092f\u0935\u0915\u094d\u0924\u093e \u0914\u0930 \u090f\u0915 \u092a\u094d\u0930\u0924\u093f\u0915\u094d\u0930\u093f\u092f\u093e \u091a\u0930 \u0915\u0947 \u092e\u093e\u0928\u094b\u0902 \u0915\u094b \u0930\u0916\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0926\u094b NumPy \u0938\u0930\u0923\u093f\u092f\u093e\u0901 \u092c\u0928\u093e\u090f\u0901:<\/span> <\/p>\n

 import<\/span> matplotlib. pyplot<\/span> as<\/span> plt\nimport<\/span> numpy as<\/span> np\n\n#define predictor and response variables\n<\/span>x = np. array<\/span> ([2, 3, 4, 5, 6, 7, 7, 8, 9, 11, 12])\ny = np. array<\/span> ([18, 16, 15, 17, 20, 23, 25, 28, 31, 30, 29])\n\n#create scatterplot to visualize relationship between x and y\n<\/span>plt. scatter<\/span> (x,y)\n<\/strong><\/pre>\n
\"\"<\/p>\n
 \u0938\u094d\u0915\u0948\u091f\u0930\u092a\u094d\u0932\u0949\u091f \u0938\u0947, \u0939\u092e \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f x \u0914\u0930 y \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927 \u0930\u0948\u0916\u093f\u0915 \u0928\u0939\u0940\u0902 \u0939\u0948\u0964<\/span><\/p>\n
 \u0907\u0938\u0932\u093f\u090f \u0926\u094b \u091a\u0930\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0917\u0948\u0930-\u0930\u0948\u0916\u093f\u0915 \u0938\u0902\u092c\u0902\u0927 \u0915\u094b \u092a\u0915\u0921\u093c\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0921\u0947\u091f\u093e \u092e\u0947\u0902 \u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u092e\u0949\u0921\u0932 \u0915\u094b \u092b\u093f\u091f \u0915\u0930\u0928\u093e \u090f\u0915 \u0905\u091a\u094d\u091b\u093e \u0935\u093f\u091a\u093e\u0930 \u0939\u0948\u0964<\/span><\/p>\n
 \u091a\u0930\u0923 2: \u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u092e\u0949\u0921\u0932 \u0915\u094b \u092b\u093c\u093f\u091f \u0915\u0930\u0947\u0902<\/strong><\/span><\/h2>\n
 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0915\u094b\u0921 \u0926\u093f\u0916\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0907\u0938 \u0921\u0947\u091f\u093e \u0938\u0947\u091f \u092e\u0947\u0902 \u0921\u093f\u0917\u094d\u0930\u0940 3 \u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u092e\u0949\u0921\u0932 \u0915\u094b \u092b\u093f\u091f \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0938\u094d\u0915\u0947\u0932\u0947\u0930 \u092b\u093c\u0902\u0915\u094d\u0936\u0902\u0938 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902:<\/span><\/p>\n
 from<\/span> sklearn. preprocessing<\/span> import<\/span> PolynomialFeatures\nfrom<\/span> sklearn. linear_model<\/span> import<\/span> LinearRegression\n\n#specify degree of 3 for polynomial regression model\n#include bias=False means don't force y-intercept to equal zero<\/span>\npoly = PolynomialFeatures(degree= 3<\/span> , include_bias= False<\/span> )\n\n#reshape data to work properly with sklearn\n<\/span>poly_features = poly. fit_transform<\/span> ( x.reshape<\/span> (-1, 1))\n\n#fit polynomial regression model\n<\/span>poly_reg_model = LinearRegression()\npoly_reg_model. fit<\/span> (poly_features,y)\n\n#display model coefficients\n<\/span>print<\/span> (poly_reg_model. intercept_<\/span> , poly_reg_model. coef_<\/span> )\n\n33.62640037532282 [-11.83877127 2.25592957 -0.10889554]\n<\/strong><\/span><\/pre>\n
 \u0905\u0902\u0924\u093f\u092e \u092a\u0902\u0915\u094d\u0924\u093f \u092e\u0947\u0902 \u0926\u093f\u0916\u093e\u090f \u0917\u090f \u092e\u0949\u0921\u0932 \u0917\u0941\u0923\u093e\u0902\u0915\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947, \u0939\u092e \u092b\u093f\u091f \u0915\u093f\u090f \u0917\u090f \u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u094b \u0928\u093f\u092e\u094d\u0928\u093e\u0928\u0941\u0938\u093e\u0930 \u0932\u093f\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/span><\/p>\n
 y = -0.109x 3<\/sup> + 2.256x 2<\/sup> \u2013 11.839x + 33.626<\/span><\/p>\n
 \u0907\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u092a\u0942\u0930\u094d\u0935\u093e\u0928\u0941\u092e\u093e\u0928\u093f\u0924 \u091a\u0930 \u0915\u0947 \u0926\u093f\u090f \u0917\u090f \u092e\u093e\u0928 \u0915\u094b \u0926\u0947\u0916\u0924\u0947 \u0939\u0941\u090f \u092a\u094d\u0930\u0924\u093f\u0915\u094d\u0930\u093f\u092f\u093e \u091a\u0930 \u0915\u0947 \u0905\u092a\u0947\u0915\u094d\u0937\u093f\u0924 \u092e\u0942\u0932\u094d\u092f \u0915\u094b \u0916\u094b\u091c\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n
 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u092f\u0926\u093f x 4 \u0939\u0948, \u0924\u094b \u092a\u094d\u0930\u0924\u093f\u0915\u094d\u0930\u093f\u092f\u093e \u091a\u0930, y \u0915\u0947 \u0932\u093f\u090f \u0905\u092a\u0947\u0915\u094d\u0937\u093f\u0924 \u092e\u093e\u0928 15.39 \u0939\u094b\u0917\u093e:<\/span><\/p>\n
 y = -0.109(4) 3<\/sup> + 2.256(4) 2<\/sup> \u2013 11.839(4) + 33.626= 15.39<\/span><\/p>\n
 \u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0902<\/strong> : \u090f\u0915 \u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u092e\u0949\u0921\u0932 \u0915\u094b \u090f\u0915 \u0905\u0932\u0917 \u0921\u093f\u0917\u094d\u0930\u0940 \u0915\u0947 \u0938\u093e\u0925 \u092b\u093f\u091f \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u092c\u0938 PolynomialFeatures()<\/strong> \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u092e\u0947\u0902 \u0921\u093f\u0917\u094d\u0930\u0940<\/strong> \u0924\u0930\u094d\u0915 \u0915\u093e \u092e\u093e\u0928 \u092c\u0926\u0932\u0947\u0902\u0964<\/span><\/p>\n
 \u091a\u0930\u0923 3: \u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u092e\u0949\u0921\u0932 \u0915\u0940 \u0915\u0932\u094d\u092a\u0928\u093e \u0915\u0930\u0947\u0902<\/span><\/strong><\/h2>\n
 \u0905\u0902\u0924 \u092e\u0947\u0902, \u0939\u092e \u092e\u0942\u0932 \u0921\u0947\u091f\u093e \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u092a\u0930 \u092b\u093f\u091f \u0915\u093f\u090f \u0917\u090f \u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u092e\u0949\u0921\u0932 \u0915\u0940 \u0915\u0932\u094d\u092a\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0938\u0930\u0932 \u092a\u094d\u0932\u0949\u091f \u092c\u0928\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/span><\/span> <\/p>\n
 #use model to make predictions on response variable\n<\/span>y_predicted = poly_reg_model. predict<\/span> (poly_features)\n\n#create scatterplot of x vs. y\n<\/span>plt. scatter<\/span> (x,y)\n\n#add line to show fitted polynomial regression model\n<\/span>plt. plot<\/span> (x,y_predicted,color=' purple<\/span> ')\n<\/strong><\/span><\/pre>\n
\"\"<\/p>\n
 \u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0902<\/strong> : \u0906\u092a \u0938\u094d\u0915\u0947\u0932\u0947\u0930 \u092a\u0949\u0932\u0940\u0928\u094b\u092e\u093f\u092f\u0932\u092b\u0940\u091a\u0930\u094d\u0938()<\/strong> \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u0947 \u0932\u093f\u090f \u092a\u0942\u0930\u094d\u0923 \u0926\u0938\u094d\u0924\u093e\u0935\u0947\u091c\u093c \u092f\u0939\u093e\u0902<\/a> \u092a\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/span><\/p>\n
 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924 \u0938\u0902\u0938\u093e\u0927\u0928<\/span><\/strong><\/span><\/h2>\n
 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u091f\u094d\u092f\u0942\u091f\u094b\u0930\u093f\u092f\u0932 \u092c\u0924\u093e\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0938\u094d\u0915\u0947\u0932\u0947\u0930\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0905\u0928\u094d\u092f \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0915\u093e\u0930\u094d\u092f \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902:<\/span><\/p>\n
 \u0938\u094d\u0915\u0947\u0932\u0947\u0930\u0928 \u0938\u0947 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u0917\u0941\u0923\u093e\u0902\u0915 \u0915\u0948\u0938\u0947 \u0928\u093f\u0915\u093e\u0932\u0947\u0902<\/a>
 \u0938\u094d\u0915\u0947\u0932\u0947\u0930 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0938\u0902\u0924\u0941\u0932\u093f\u0924 \u092a\u0930\u093f\u0936\u0941\u0926\u094d\u0927\u0924\u093e \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902<\/a>
 \u0938\u094d\u0915\u0947\u0932\u0947\u0930\u0928 \u092e\u0947\u0902 \u0935\u0930\u094d\u0917\u0940\u0915\u0930\u0923 \u0930\u093f\u092a\u094b\u0930\u094d\u091f \u0915\u0940 \u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
\u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u090f\u0915 \u0910\u0938\u0940 \u0924\u0915\u0928\u0940\u0915 \u0939\u0948 \u091c\u093f\u0938\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0939\u092e \u0924\u092c \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u091c\u092c \u090f\u0915 \u092a\u0942\u0930\u094d\u0935\u0938\u0942\u091a\u0915 \u091a\u0930 \u0914\u0930 \u090f\u0915 \u092a\u094d\u0930\u0924\u093f\u0915\u094d\u0930\u093f\u092f\u093e \u091a\u0930 \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927 \u0905\u0930\u0947\u0916\u0940\u092f \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u0928\u093f\u092e\u094d\u0928 \u0930\u0942\u092a \u0932\u0947\u0924\u093e \u0939\u0948: \u0935\u093e\u0908 = \u03b2 0 + \u03b2 1 \u090f\u0915\u094d\u0938 + \u03b2 2 \u090f\u0915\u094d\u0938 2 + \u2026 + \u03b2 \u090f\u091a 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