{"id":1648,"date":"2023-07-25T12:50:55","date_gmt":"2023-07-25T12:50:55","guid":{"rendered":"https:\/\/statorials.org\/hi\/%e0%a4%aa%e0%a4%be%e0%a4%af%e0%a4%a5%e0%a4%a8-%e0%a4%b5%e0%a4%95%e0%a5%8d%e0%a4%b0-%e0%a4%ab%e0%a4%bf%e0%a4%9f%e0%a4%bf%e0%a4%82%e0%a4%97\/"},"modified":"2023-07-25T12:50:55","modified_gmt":"2023-07-25T12:50:55","slug":"%e0%a4%aa%e0%a4%be%e0%a4%af%e0%a4%a5%e0%a4%a8-%e0%a4%b5%e0%a4%95%e0%a5%8d%e0%a4%b0-%e0%a4%ab%e0%a4%bf%e0%a4%9f%e0%a4%bf%e0%a4%82%e0%a4%97","status":"publish","type":"post","link":"https:\/\/statorials.org\/hi\/%e0%a4%aa%e0%a4%be%e0%a4%af%e0%a4%a5%e0%a4%a8-%e0%a4%b5%e0%a4%95%e0%a5%8d%e0%a4%b0-%e0%a4%ab%e0%a4%bf%e0%a4%9f%e0%a4%bf%e0%a4%82%e0%a4%97\/","title":{"rendered":"\u092a\u093e\u092f\u0925\u0928 \u092e\u0947\u0902 \u0915\u0930\u094d\u0935 \u092b\u093f\u091f\u093f\u0902\u0917 (\u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0938\u093e\u0925)"},"content":{"rendered":"

<\/p>\n

\n

\u0905\u0915\u094d\u0938\u0930 \u0906\u092a \u092a\u093e\u092f\u0925\u0928 \u092e\u0947\u0902 \u0921\u0947\u091f\u093e\u0938\u0947\u091f \u092e\u0947\u0902 \u090f\u0915 \u0915\u0930\u094d\u0935 \u092b\u093f\u091f \u0915\u0930\u0928\u093e \u091a\u093e\u0939 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/span> <\/p>\n

\"\"<\/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 \u092c\u0924\u093e\u0924\u093e \u0939\u0948 \u0915\u093f numpy.polyfit()<\/a> \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u092a\u093e\u092f\u0925\u0928 \u092e\u0947\u0902 \u0921\u0947\u091f\u093e \u092e\u0947\u0902 \u0915\u0930\u094d\u0935\u094d\u0938 \u0915\u094b \u0915\u0948\u0938\u0947 \u092b\u093f\u091f \u0915\u093f\u092f\u093e \u091c\u093e\u090f \u0914\u0930 \u092f\u0939 \u0915\u0948\u0938\u0947 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u090f \u0915\u093f \u0915\u094c\u0928 \u0938\u093e \u0915\u0930\u094d\u0935 \u0921\u0947\u091f\u093e \u0915\u0947 \u0932\u093f\u090f \u0938\u092c\u0938\u0947 \u0909\u092a\u092f\u0941\u0915\u094d\u0924 \u0939\u0948\u0964<\/span><\/p>\n

\u091a\u0930\u0923 1: \u0921\u0947\u091f\u093e \u092c\u0928\u093e\u090f\u0902 \u0914\u0930 \u0935\u093f\u091c\u093c\u0941\u0905\u0932\u093e\u0907\u091c\u093c \u0915\u0930\u0947\u0902<\/strong><\/span><\/h3>\n

\u0906\u0907\u090f \u090f\u0915 \u0928\u0915\u0932\u0940 \u0921\u0947\u091f\u093e\u0938\u0947\u091f \u092c\u0928\u093e\u0915\u0930 \u0936\u0941\u0930\u0941\u0906\u0924 \u0915\u0930\u0947\u0902, \u092b\u093f\u0930 \u0921\u0947\u091f\u093e \u0915\u0940 \u0915\u0932\u094d\u092a\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0938\u094d\u0915\u0948\u091f\u0930\u092a\u094d\u0932\u0949\u091f \u092c\u0928\u093e\u090f\u0902:<\/span> <\/p>\n

 import<\/span> pandas as<\/span> pd\nimport<\/span> matplotlib. pyplot<\/span> as<\/span> plt\n\n#createDataFrame\n<\/span>df = pd. DataFrame<\/span> ({' x<\/span> ': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],\n                   ' y<\/span> ': [3, 14, 23, 25, 23, 15, 9, 5, 9, 13, 17, 24, 32, 36, 46]})\n\n#create scatterplot of x vs. y\n<\/span>plt. scatter<\/span> (df. x<\/span> , df. y<\/span> )<\/strong> <\/pre>\n
\"\"<\/p>\n
 \u091a\u0930\u0923 2: \u090f\u0915\u093e\u0927\u093f\u0915 \u0935\u0915\u094d\u0930 \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0915\u0930\u0947\u0902<\/strong><\/span><\/h3>\n
 \u0906\u0907\u090f \u092b\u093f\u0930 \u0921\u0947\u091f\u093e \u092e\u0947\u0902 \u0915\u0908 \u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u092e\u0949\u0921\u0932 \u092b\u093f\u091f \u0915\u0930\u0947\u0902 \u0914\u0930 \u090f\u0915 \u0939\u0940 \u092a\u094d\u0932\u0949\u091f \u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092e\u0949\u0921\u0932 \u0915\u0947 \u0935\u0915\u094d\u0930 \u0915\u0940 \u0915\u0932\u094d\u092a\u0928\u093e \u0915\u0930\u0947\u0902:<\/span> <\/p>\n
 import<\/span> numpy as<\/span> np\n\n#fit polynomial models up to degree 5\n<\/span>model1 = np. poly1d<\/span> (np. polyfit<\/span> (df. x<\/span> , df. y<\/span> , 1))\nmodel2 = np. poly1d<\/span> (np. polyfit<\/span> (df. x<\/span> , df. y<\/span> , 2))\nmodel3 = np. poly1d<\/span> (np. polyfit<\/span> (df. x<\/span> , df. y<\/span> , 3))\nmodel4 = np. poly1d<\/span> (np. polyfit<\/span> (df. x<\/span> , df. y<\/span> , 4))\nmodel5 = np. poly1d<\/span> (np. polyfit<\/span> (df. x<\/span> , df. y<\/span> , 5))\n\n#create scatterplot\n<\/span>polyline = np. linspace<\/span> (1, 15, 50)\nplt. scatter<\/span> (df. x<\/span> , df. y<\/span> )\n\n#add fitted polynomial lines to scatterplot \n<\/span>plt. plot<\/span> (polyline, model1(polyline), color=' green<\/span> ')\nplt. plot<\/span> (polyline, model2(polyline), color=' red<\/span> ')\nplt. plot<\/span> (polyline, model3(polyline), color=' purple<\/span> ')\nplt. plot<\/span> (polyline, model4(polyline), color=' blue<\/span> ')\nplt. plot<\/span> (polyline, model5(polyline), color=' orange<\/span> ')\nplt. show<\/span> ()\n<\/span><\/span><\/strong><\/pre>\n
\"\"<\/p>\n
 \u092f\u0939 \u092e\u093e\u0928 \u0939\u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u093f\u0915\u094d\u0930\u093f\u092f\u093e \u091a\u0930 \u092e\u0947\u0902 \u092d\u093f\u0928\u094d\u0928\u0924\u093e \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0936\u0924 \u092c\u0924\u093e\u0924\u093e \u0939\u0948 \u091c\u093f\u0938\u0947 \u092e\u0949\u0921\u0932 \u092e\u0947\u0902 \u092d\u0935\u093f\u0937\u094d\u092f\u0935\u0915\u094d\u0924\u093e \u091a\u0930 \u0926\u094d\u0935\u093e\u0930\u093e \u0938\u092e\u091d\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0947 \u092d\u0935\u093f\u0937\u094d\u092f\u0935\u0915\u094d\u0924\u093e \u091a\u0930 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u0932\u093f\u090f \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n
 #define function to calculate adjusted r-squared\ndef<\/span> adjR(x, y, degree):\n    results = {}\n    coeffs = np. polyfit<\/span> (x, y, degree)\n    p = np. poly1d<\/span> (coeffs)\n    yhat = p(x)\n    ybar = np. sum<\/span> (y)\/len(y)\n    ssreg = np. sum<\/span> ((yhat-ybar)**2)\n    sstot = np. sum<\/span> ((y - ybar)**2)\n    results[' r_squared<\/span> '] = 1- (((1-(ssreg\/sstot))*(len(y)-1))\/(len(y)-degree-1))\n\n    return<\/span> results<\/span>\n\n#calculated adjusted R-squared of each model\n<\/span>adjR(df. x<\/span> , df. y<\/span> , 1)\nadjR(df. x<\/span> , df. y<\/span> , 2)\nadjR(df. x<\/span> , df. y<\/span> , 3)\nadjR(df. x<\/span> , df. y<\/span> , 4)\nadjR(df. x<\/span> , df. y<\/span> , 5)\n\n{'r_squared': 0.3144819}\n{'r_squared': 0.5186706}\n{'r_squared': 0.7842864}\n{'r_squared': 0.9590276}\n{'r_squared': 0.9549709}\n<\/strong><\/pre>\n
 \u092a\u0930\u093f\u0923\u093e\u092e \u0938\u0947, \u0939\u092e \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0909\u091a\u094d\u091a\u0924\u092e \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0906\u0930-\u0935\u0930\u094d\u0917 \u0935\u093e\u0932\u093e \u092e\u0949\u0921\u0932 \u091a\u094c\u0925\u0940 \u0921\u093f\u0917\u094d\u0930\u0940 \u092c\u0939\u0941\u092a\u0926 \u0939\u0948, \u091c\u093f\u0938\u0915\u093e \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0906\u0930-\u0935\u0930\u094d\u0917 0.959<\/strong> \u0939\u0948\u0964<\/span><\/p>\n
 \u091a\u0930\u0923 3: \u0905\u0902\u0924\u093f\u092e \u0935\u0915\u094d\u0930 \u0915\u0940 \u0915\u0932\u094d\u092a\u0928\u093e \u0915\u0930\u0947\u0902<\/strong><\/span><\/h3>\n
 \u0905\u0902\u0924 \u092e\u0947\u0902, \u0939\u092e \u091a\u094c\u0925\u0940 \u0921\u093f\u0917\u094d\u0930\u0940 \u092c\u0939\u0941\u092a\u0926 \u092e\u0949\u0921\u0932 \u0915\u0947 \u0935\u0915\u094d\u0930 \u0915\u0947 \u0938\u093e\u0925 \u090f\u0915 \u0938\u094d\u0915\u0948\u091f\u0930 \u092a\u094d\u0932\u0949\u091f \u092c\u0928\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/span> <\/p>\n
 #fit fourth-degree polynomial\n<\/span>model4 = np. poly1d<\/span> (np. polyfit<\/span> (df. x<\/span> , df. y<\/span> , 4))\n\n#define scatterplot\n<\/span>polyline = np. linspace<\/span> (1, 15, 50)\nplt. scatter<\/span> (df. x<\/span> , df. y<\/span> )\n\n#add fitted polynomial curve to scatterplot\n<\/span>plt. plot<\/span> (polyline, model4(polyline), ' --<\/span> ', color=' red<\/span> ')\nplt. show<\/span> ()\n<\/strong><\/pre>\n
\"\"<\/p>\n
 \u0939\u092e print()<\/strong> \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0907\u0938 \u092a\u0902\u0915\u094d\u0924\u093f \u0915\u0947 \u0932\u093f\u090f \u0938\u092e\u0940\u0915\u0930\u0923 \u092d\u0940 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/span><\/p>\n
 print<\/span> (model4)\n\n          4 3 2\n-0.01924x + 0.7081x - 8.365x + 35.82x - 26.52\n<\/strong><\/pre>\n
 \u0935\u0915\u094d\u0930 \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u0948:<\/span><\/p>\n
 y = -0.01924x 4<\/sup> + 0.7081x 3<\/sup> \u2013 8.365x 2<\/sup> + 35.82x \u2013 26.52<\/span><\/p>\n
 \u0939\u092e \u092e\u0949\u0921\u0932 \u092e\u0947\u0902 \u092d\u0935\u093f\u0937\u094d\u092f\u0935\u0915\u094d\u0924\u093e \u091a\u0930 \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u0915\u094d\u0930\u093f\u092f\u093e \u091a\u0930<\/a> \u0915\u0947 \u092e\u0942\u0932\u094d\u092f \u0915\u0940 \u092d\u0935\u093f\u0937\u094d\u092f\u0935\u093e\u0923\u0940 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0907\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f \u092f\u0926\u093f x<\/em> = 4 \u0939\u0948 \u0924\u094b \u0939\u092e \u0905\u0928\u0941\u092e\u093e\u0928 \u0932\u0917\u093e\u090f\u0902\u0917\u0947 \u0915\u093f y<\/em> = 23.32<\/strong> :<\/span><\/p>\n
 y = -0.0192(4) 4<\/sup> + 0.7081(4) 3<\/sup> \u2013 8.365(4) 2<\/sup> + 35.82(4) \u2013 26.52 = 23.32<\/span><\/p>\n
 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924 \u0938\u0902\u0938\u093e\u0927\u0928<\/strong><\/span><\/h3>\n
 \u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u0915\u093e \u090f\u0915 \u092a\u0930\u093f\u091a\u092f
<\/a> \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<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
\u0905\u0915\u094d\u0938\u0930 \u0906\u092a \u092a\u093e\u092f\u0925\u0928 \u092e\u0947\u0902 \u0921\u0947\u091f\u093e\u0938\u0947\u091f \u092e\u0947\u0902 \u090f\u0915 \u0915\u0930\u094d\u0935 \u092b\u093f\u091f \u0915\u0930\u0928\u093e \u091a\u093e\u0939 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u091a\u0930\u0923-\u0926\u0930-\u091a\u0930\u0923 \u0909\u0926\u093e\u0939\u0930\u0923 \u092c\u0924\u093e\u0924\u093e \u0939\u0948 \u0915\u093f numpy.polyfit() \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u092a\u093e\u092f\u0925\u0928 \u092e\u0947\u0902 \u0921\u0947\u091f\u093e \u092e\u0947\u0902 \u0915\u0930\u094d\u0935\u094d\u0938 \u0915\u094b \u0915\u0948\u0938\u0947 \u092b\u093f\u091f \u0915\u093f\u092f\u093e \u091c\u093e\u090f \u0914\u0930 \u092f\u0939 \u0915\u0948\u0938\u0947 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u090f \u0915\u093f \u0915\u094c\u0928 \u0938\u093e \u0915\u0930\u094d\u0935 \u0921\u0947\u091f\u093e \u0915\u0947 \u0932\u093f\u090f \u0938\u092c\u0938\u0947 \u0909\u092a\u092f\u0941\u0915\u094d\u0924 \u0939\u0948\u0964 \u091a\u0930\u0923 1: \u0921\u0947\u091f\u093e \u092c\u0928\u093e\u090f\u0902 \u0914\u0930 […]<\/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":[],"class_list":["post-1648","post","type-post","status-publish","format-standard","hentry","category-3"],"yoast_head":"\n\u092a\u093e\u092f\u0925\u0928 \u092e\u0947\u0902 \u0915\u0930\u094d\u0935 \u092b\u093f\u091f\u093f\u0902\u0917 (\u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0938\u093e\u0925) - \u0938\u094d\u091f\u0947\u091f\u094b\u0932\u0949\u091c\u0940<\/title>\n<meta name=\"description\" content=\"\u092f\u0939 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