{"id":475,"date":"2023-07-29T19:05:27","date_gmt":"2023-07-29T19:05:27","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%86%e0%a4%b0\/"},"modified":"2023-07-29T19:05:27","modified_gmt":"2023-07-29T19:05:27","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%86%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%86%e0%a4%b0\/","title":{"rendered":"\u0906\u0930 \u092e\u0947\u0902 \u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 (\u091a\u0930\u0923 \u0926\u0930 \u091a\u0930\u0923)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/hi\/\u092c\u0939\u0941\u092a\u0926-\u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928-1\/\" target=\"_blank\" rel=\"noopener noreferrer\">\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 <a href=\"https:\/\/statorials.org\/hi\/\u091a\u0930-\u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e\u0924\u094d\u092e\u0915-\u092a\u094d\u0930\u0924\u093f\u0915\u094d\u0930\u093f\u092f\u093e\u090f\u0901\/\" target=\"_blank\" rel=\"noopener noreferrer\">\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<p> <span style=\"color: #000000;\">\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<p> <span style=\"color: #000000;\">\u0935\u093e\u0908 = \u03b2 <sub>0<\/sub> <sup>+<\/sup> \u03b2 <sub>1<\/sub> \u090f\u0915\u094d\u0938 + \u03b2 <sub>2<\/sub> \u090f\u0915\u094d\u0938 <sup>2<\/sup> + \u2026 + \u03b2 <sub>\u090f\u091a<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u091c\u0939\u093e\u0901 <em>h<\/em> \u092c\u0939\u0941\u092a\u0926 \u0915\u0940 &#8220;\u0921\u093f\u0917\u094d\u0930\u0940&#8221; \u0939\u0948\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u092f\u0939 \u091f\u094d\u092f\u0942\u091f\u094b\u0930\u093f\u092f\u0932 \u0906\u0930 \u092e\u0947\u0902 \u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902 \u0907\u0938\u0915\u093e \u091a\u0930\u0923-\u0926\u0930-\u091a\u0930\u0923 \u0909\u0926\u093e\u0939\u0930\u0923 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u091a\u0930\u0923 1: \u0921\u0947\u091f\u093e \u092c\u0928\u093e\u090f\u0902<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0907\u0938 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e \u090f\u0915 \u0921\u0947\u091f\u093e\u0938\u0947\u091f \u092c\u0928\u093e\u090f\u0902\u0917\u0947 \u091c\u093f\u0938\u092e\u0947\u0902 50 \u091b\u093e\u0924\u094d\u0930\u094b\u0902 \u0915\u0940 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0932\u093f\u090f \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u093f\u090f \u0917\u090f \u0918\u0902\u091f\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0914\u0930 \u0905\u0902\u0924\u093f\u092e \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u0917\u094d\u0930\u0947\u0921 \u0936\u093e\u092e\u093f\u0932 \u0939\u094b\u0917\u093e:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#make this example reproducible<\/span>\nset.seed(1)\n\n<span style=\"color: #008080;\">#create dataset\n<\/span>df &lt;- data.frame(hours = <span style=\"color: #3366ff;\">runif<\/span> (50, 5, 15), score=50)\ndf$score = df$score + df$hours^3\/150 + df$hours* <span style=\"color: #3366ff;\">runif<\/span> (50, 1, 2)\n\n<span style=\"color: #008080;\">#view first six rows of data\n<\/span>head(data)\n\n      hours score\n1 7.655087 64.30191\n2 8.721239 70.65430\n3 10.728534 73.66114\n4 14.082078 86.14630\n5 7.016819 59.81595\n6 13.983897 83.60510\n<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>\u091a\u0930\u0923 2: \u0921\u0947\u091f\u093e \u0915\u094b \u0935\u093f\u091c\u093c\u0941\u0905\u0932\u093e\u0907\u091c\u093c \u0915\u0930\u0947\u0902<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0921\u0947\u091f\u093e \u092e\u0947\u0902 \u090f\u0915 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u092e\u0949\u0921\u0932 \u092b\u093f\u091f \u0915\u0930\u0928\u0947 \u0938\u0947 \u092a\u0939\u0932\u0947, \u0906\u0907\u090f \u092a\u0939\u0932\u0947 \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u093f\u090f \u0917\u090f \u0918\u0902\u091f\u094b\u0902 \u0914\u0930 \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u0938\u094d\u0915\u094b\u0930 \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927 \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<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #993300;\">library<\/span> (ggplot2)\n\nggplot(df, <span style=\"color: #3366ff;\">aes<\/span> (x=hours, y=score)) +\n  geom_point()<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12001 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/poly1-1.png\" alt=\"\" width=\"457\" height=\"450\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u0939\u092e \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0921\u0947\u091f\u093e \u092e\u0947\u0902 \u0925\u094b\u0921\u093c\u093e \u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u0938\u0902\u092c\u0902\u0927 \u0939\u0948, \u091c\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u0938\u0930\u0932 \u0930\u0948\u0916\u093f\u0915 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u092e\u0947\u0902 \u0921\u0947\u091f\u093e \u0915\u094b \u092c\u0947\u0939\u0924\u0930 \u0922\u0902\u0917 \u0938\u0947 \u092b\u093f\u091f \u0915\u0930 \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">\u091a\u0930\u0923 3: \u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u092e\u0949\u0921\u0932 \u092b\u093c\u093f\u091f \u0915\u0930\u0947\u0902<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">\u0907\u0938\u0915\u0947 \u092c\u093e\u0926, \u0939\u092e \u0921\u093f\u0917\u094d\u0930\u0940 <em>h<\/em> = 1\u20265 \u0915\u0947 \u0938\u093e\u0925 \u092a\u093e\u0902\u091a \u0905\u0932\u0917-\u0905\u0932\u0917 \u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u092e\u0949\u0921\u0932 \u092b\u093f\u091f \u0915\u0930\u0947\u0902\u0917\u0947 \u0914\u0930 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092e\u0949\u0921\u0932 \u0915\u0947 \u0932\u093f\u090f MSE \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f k = 10 \u092c\u093e\u0930 \u0915\u0947-\u0917\u0941\u0928\u093e \u0915\u094d\u0930\u0949\u0938-\u0938\u0924\u094d\u092f\u093e\u092a\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0917\u0947:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#randomly shuffle data\n<\/span>df.shuffled &lt;- df[ <span style=\"color: #3366ff;\">sample<\/span> ( <span style=\"color: #3366ff;\">nrow<\/span> (df)),]\n\n<span style=\"color: #008080;\">#define number of folds to use for k-fold cross-validation\n<\/span>K &lt;- 10 \n\n<span style=\"color: #008080;\">#define degree of polynomials to fit\n<\/span>degree &lt;- 5\n\n<span style=\"color: #008080;\">#create k equal-sized folds\n<\/span>folds &lt;- cut( <span style=\"color: #3366ff;\">seq<\/span> (1, <span style=\"color: #3366ff;\">nrow<\/span> (df.shuffled)), breaks=K, labels= <span style=\"color: #008000;\">FALSE<\/span> )\n\n<span style=\"color: #008080;\">#create object to hold MSE's of models\n<\/span>mse = matrix(data=NA,nrow=K,ncol=degree)\n\n<span style=\"color: #008080;\">#Perform K-fold cross validation\n<\/span><span style=\"color: #008000;\">for<\/span> (i <span style=\"color: #008000;\">in<\/span> 1:K){\n    \n<span style=\"color: #008080;\">#define training and testing data\n<\/span>testIndexes &lt;- <span style=\"color: #3366ff;\">which<\/span> (folds==i,arr.ind= <span style=\"color: #008000;\">TRUE<\/span> )\n    testData &lt;- df.shuffled[testIndexes, ]\n    trainData &lt;- df.shuffled[-testIndexes, ]\n    \n<span style=\"color: #008080;\">#use k-fold cv to evaluate models\n<\/span>for (j in 1:degree){\n        fit.train = <span style=\"color: #3366ff;\">lm<\/span> (score ~ <span style=\"color: #3366ff;\">poly<\/span> (hours,d), data=trainData)\n        fit.test = <span style=\"color: #3366ff;\">predict<\/span> (fit.train, newdata=testData)\n        mse[i,j] = <span style=\"color: #3366ff;\">mean<\/span> ((fit.test-testData$score)^2) \n    }\n}\n\n<span style=\"color: #008080;\">#find MSE for each degree \n<\/span>colMeans(mse)\n\n[1] 9.802397 8.748666 9.601865 10.592569 13.545547\n<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">\u092a\u0930\u093f\u0923\u093e\u092e \u0938\u0947 \u0939\u092e \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092e\u0949\u0921\u0932 \u0915\u0947 \u0932\u093f\u090f \u090f\u092e\u090f\u0938\u0908 \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u0921\u093f\u0917\u094d\u0930\u0940 \u090f\u091a = 1: <strong>9.80<\/strong> \u0915\u0947 \u0938\u093e\u0925 \u090f\u092e\u090f\u0938\u0908 \u092a\u0930\u0940\u0915\u094d\u0937\u0923<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0921\u093f\u0917\u094d\u0930\u0940 \u090f\u091a = 2: <strong>8.75<\/strong> \u0915\u0947 \u0938\u093e\u0925 \u090f\u092e\u090f\u0938\u0908 \u092a\u0930\u0940\u0915\u094d\u0937\u0923<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0921\u093f\u0917\u094d\u0930\u0940 \u090f\u091a = 3: <strong>9.60<\/strong> \u0915\u0947 \u0938\u093e\u0925 \u090f\u092e\u090f\u0938\u0908 \u092a\u0930\u0940\u0915\u094d\u0937\u0923<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0921\u093f\u0917\u094d\u0930\u0940 \u090f\u091a = 4: <strong>10.59<\/strong> \u0915\u0947 \u0938\u093e\u0925 \u090f\u092e\u090f\u0938\u0908 \u092a\u0930\u0940\u0915\u094d\u0937\u0923<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0921\u093f\u0917\u094d\u0930\u0940 \u090f\u091a = 5: <strong>13.55<\/strong> \u0915\u0947 \u0938\u093e\u0925 \u090f\u092e\u090f\u0938\u0908 \u092a\u0930\u0940\u0915\u094d\u0937\u0923<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u0938\u092c\u0938\u0947 \u0915\u092e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u090f\u092e\u090f\u0938\u0908 \u0935\u093e\u0932\u093e \u092e\u0949\u0921\u0932 \u0921\u093f\u0917\u094d\u0930\u0940 <em>\u090f\u091a<\/em> = 2 \u0915\u0947 \u0938\u093e\u0925 \u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u092e\u0949\u0921\u0932 \u092c\u0928 \u0917\u092f\u093e\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u092f\u0939 \u092e\u0942\u0932 \u0938\u094d\u0915\u0948\u091f\u0930\u092a\u094d\u0932\u0949\u091f \u0938\u0947 \u0939\u092e\u093e\u0930\u0947 \u0905\u0902\u0924\u0930\u094d\u091c\u094d\u091e\u093e\u0928 \u0938\u0947 \u092e\u0947\u0932 \u0916\u093e\u0924\u093e \u0939\u0948: \u090f\u0915 \u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u092e\u0949\u0921\u0932 \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<h3> <strong><span style=\"color: #000000;\">\u091a\u0930\u0923 4: \u0905\u0902\u0924\u093f\u092e \u092e\u0949\u0921\u0932 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0947\u0902<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">\u0905\u0902\u0924 \u092e\u0947\u0902, \u0939\u092e \u0938\u0930\u094d\u0935\u094b\u0924\u094d\u0924\u092e \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u0928 \u0915\u0930\u0928\u0947 \u0935\u093e\u0932\u0947 \u092e\u0949\u0921\u0932 \u0915\u0947 \u0917\u0941\u0923\u093e\u0902\u0915 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#fit best model<\/span>\nbest = <span style=\"color: #3366ff;\">lm<\/span> (score ~ <span style=\"color: #3366ff;\">poly<\/span> (hours,2, raw= <span style=\"color: #008000;\">T<\/span> ), data=df)\n\n<span style=\"color: #008080;\">#view summary of best model<\/span>\nsummary(best)\n\nCall:\nlm(formula = score ~ poly(hours, 2, raw = T), data = df)\n\nResiduals:\n    Min 1Q Median 3Q Max \n-5.6589 -2.0770 -0.4599 2.5923 4.5122 \n\nCoefficients:\n                         Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) 54.00526 5.52855 9.768 6.78e-13 ***\npoly(hours, 2, raw = T)1 -0.07904 1.15413 -0.068 0.94569    \npoly(hours, 2, raw = T)2 0.18596 0.05724 3.249 0.00214 ** \n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u092a\u0930\u093f\u0923\u093e\u092e \u0938\u0947, \u0939\u092e \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0905\u0902\u0924\u093f\u092e \u092b\u093f\u091f \u092e\u0949\u0921\u0932 \u0939\u0948:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0938\u094d\u0915\u094b\u0930 = 54.00526 \u2013 0.07904*(\u0918\u0902\u091f\u0947) + 0.18596*(\u0918\u0902\u091f\u0947) <sup>2<\/sup><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0939\u092e \u0907\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u092f\u0939 \u0905\u0928\u0941\u092e\u093e\u0928 \u0932\u0917\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0915\u093f\u0938\u0940 \u091b\u093e\u0924\u094d\u0930 \u0915\u094b \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u093f\u090f \u0917\u090f \u0918\u0902\u091f\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930 \u0915\u093f\u0924\u0928\u093e \u0938\u094d\u0915\u094b\u0930 \u092e\u093f\u0932\u0947\u0917\u093e\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u090f\u0915 \u091b\u093e\u0924\u094d\u0930 \u091c\u094b 10 \u0918\u0902\u091f\u0947 \u092a\u0922\u093c\u093e\u0908 \u0915\u0930\u0924\u093e \u0939\u0948 \u0909\u0938\u0947 <strong>71.81<\/strong> \u0915\u093e \u0917\u094d\u0930\u0947\u0921 \u092e\u093f\u0932\u0928\u093e \u091a\u093e\u0939\u093f\u090f:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0938\u094d\u0915\u094b\u0930 = 54.00526 \u2013 0.07904*(10) + 0.18596*(10) <sup>2<\/sup> = 71.81<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0939\u092e \u092b\u093f\u091f \u0915\u093f\u090f \u0917\u090f \u092e\u0949\u0921\u0932 \u0915\u094b \u092f\u0939 \u0926\u0947\u0916\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092d\u0940 \u092a\u094d\u0932\u0949\u091f \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u092f\u0939 \u0915\u091a\u094d\u091a\u0947 \u0921\u0947\u091f\u093e \u092e\u0947\u0902 \u0915\u093f\u0924\u0928\u0940 \u0905\u091a\u094d\u091b\u0940 \u0924\u0930\u0939 \u092b\u093f\u091f \u092c\u0948\u0920\u0924\u093e \u0939\u0948:<\/span> <\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong>ggplot(df, <span style=\"color: #3366ff;\">aes<\/span> (x=hours, y=score)) + \n          geom_point() +\n          stat_smooth(method=' <span style=\"color: #008000;\">lm<\/span> ', formula = y ~ <span style=\"color: #3366ff;\">poly<\/span> (x,2), size = 1) + \n          xlab(' <span style=\"color: #008000;\">Hours Studied<\/span> ') +\n          ylab(' <span style=\"color: #008000;\">Score<\/span> ')<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12002 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/poly2.png\" alt=\"\u0906\u0930 \u092e\u0947\u0902 \u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928\" width=\"446\" height=\"449\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u0906\u092a \u0907\u0938 \u0909\u0926\u093e\u0939\u0930\u0923 \u092e\u0947\u0902 \u092a\u094d\u0930\u092f\u0941\u0915\u094d\u0924 \u092a\u0942\u0930\u093e \u0906\u0930 \u0915\u094b\u0921 <a href=\"https:\/\/github.com\/Statorials\/R-Guides\/blob\/main\/polynomial_regression.R\" target=\"_blank\" rel=\"noopener noreferrer\">\u092f\u0939\u093e\u0902<\/a> \u092a\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\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 \u091c\u0939\u093e\u0901 h [&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":[],"class_list":["post-475","post","type-post","status-publish","format-standard","hentry","category-3"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0906\u0930 \u092e\u0947\u0902 \u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 (\u091a\u0930\u0923 \u0926\u0930 \u091a\u0930\u0923) - \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940<\/title>\n<meta name=\"description\" content=\"\u092f\u0939 \u091f\u094d\u092f\u0942\u091f\u094b\u0930\u093f\u092f\u0932 \u090f\u0915 \u0909\u0926\u093e\u0939\u0930\u0923 \u0938\u0939\u093f\u0924, \u0906\u0930 \u092e\u0947\u0902 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