{"id":3998,"date":"2023-07-14T06:42:43","date_gmt":"2023-07-14T06:42:43","guid":{"rendered":"https:\/\/statorials.org\/hi\/%e0%a4%86%e0%a4%b0-%e0%a4%ae%e0%a5%87%e0%a4%82-%e0%a4%a4%e0%a4%96%e0%a4%bc%e0%a5%8d%e0%a4%a4%e0%a4%be-%e0%a4%aa%e0%a5%8d%e0%a4%b0%e0%a4%a4%e0%a4%bf%e0%a4%97%e0%a4%ae%e0%a4%a8\/"},"modified":"2023-07-14T06:42:43","modified_gmt":"2023-07-14T06:42:43","slug":"%e0%a4%86%e0%a4%b0-%e0%a4%ae%e0%a5%87%e0%a4%82-%e0%a4%a4%e0%a4%96%e0%a4%bc%e0%a5%8d%e0%a4%a4%e0%a4%be-%e0%a4%aa%e0%a5%8d%e0%a4%b0%e0%a4%a4%e0%a4%bf%e0%a4%97%e0%a4%ae%e0%a4%a8","status":"publish","type":"post","link":"https:\/\/statorials.org\/hi\/%e0%a4%86%e0%a4%b0-%e0%a4%ae%e0%a5%87%e0%a4%82-%e0%a4%a4%e0%a4%96%e0%a4%bc%e0%a5%8d%e0%a4%a4%e0%a4%be-%e0%a4%aa%e0%a5%8d%e0%a4%b0%e0%a4%a4%e0%a4%bf%e0%a4%97%e0%a4%ae%e0%a4%a8\/","title":{"rendered":"\u0906\u0930 \u092e\u0947\u0902 \u0938\u094d\u092a\u094d\u0932\u093e\u0907\u0928 \u0930\u093f\u0917\u094d\u0930\u0947\u0936\u0928 \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902 (\u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0938\u093e\u0925)"},"content":{"rendered":"

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\u0938\u094d\u092a\u0932\u093e\u0907\u0928 \u0930\u093f\u0917\u094d\u0930\u0947\u0936\u0928<\/strong> \u090f\u0915 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u093e \u0930\u093f\u0917\u094d\u0930\u0947\u0936\u0928 \u0939\u0948 \u091c\u093f\u0938\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0924\u092c \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u091c\u092c \u0910\u0938\u0947 \u092c\u093f\u0902\u0926\u0941 \u092f\u093e “\u0917\u093e\u0902\u0920\u0947\u0902” \u0939\u094b\u0924\u0940 \u0939\u0948\u0902 \u091c\u0939\u093e\u0902 \u0921\u0947\u091f\u093e \u092e\u0947\u0902 \u092a\u0948\u091f\u0930\u094d\u0928 \u0905\u091a\u093e\u0928\u0915 \u092c\u0926\u0932 \u091c\u093e\u0924\u093e \u0939\u0948 \u0914\u0930 \u0930\u0948\u0916\u093f\u0915 \u0930\u093f\u0917\u094d\u0930\u0947\u0936\u0928<\/a> \u0914\u0930 \u092c\u0939\u0941\u092a\u0926 \u0930\u093f\u0917\u094d\u0930\u0947\u0936\u0928<\/a> \u0921\u0947\u091f\u093e \u0915\u094b \u092b\u093f\u091f \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u094d\u092f\u093e\u092a\u094d\u0924 \u0932\u091a\u0940\u0932\u0947 \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\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 \u0906\u0930 \u092e\u0947\u0902 \u0938\u094d\u092a\u0932\u093e\u0907\u0928 \u0930\u093f\u0917\u094d\u0930\u0947\u0936\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 \u0906\u0930 \u092e\u0947\u0902 \u0926\u094b \u0935\u0947\u0930\u093f\u090f\u092c\u0932\u094d\u0938 \u0915\u0947 \u0938\u093e\u0925 \u090f\u0915 \u0921\u0947\u091f\u093e\u0938\u0947\u091f \u092c\u0928\u093e\u090f\u0902 \u0914\u0930 \u0935\u0947\u0930\u093f\u090f\u092c\u0932\u094d\u0938 \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927 \u0915\u094b \u0926\u0947\u0916\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

 #create data frame\n<\/span>df <- data. frame<\/span> (x=1:20,\n                 y=c(2, 4, 7, 9, 13, 15, 19, 16, 13, 10,\n                     11, 14, 15, 15, 16, 15, 17, 19, 18, 20))\n\n#view head of data frame\n<\/span>head(df)\n\n  xy\n1 1 2\n2 2 4\n3 3 7\n4 4 9\n5 5 13\n6 6 15\n\n#create scatterplot\n<\/span>plot(df$x, df$y, cex= 1.5<\/span> , pch= 19<\/span> )\n<\/strong><\/pre>\n
\"\"<\/p>\n
 \u0938\u094d\u092a\u0937\u094d\u091f \u0930\u0942\u092a \u0938\u0947 x \u0914\u0930 y \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927 \u0917\u0948\u0930-\u0930\u0948\u0916\u093f\u0915 \u0939\u0948 \u0914\u0930 \u0935\u0939\u093e\u0902 \u0926\u094b \u092c\u093f\u0902\u0926\u0941 \u092f\u093e “\u0928\u094b\u0921\u094d\u0938” \u092a\u094d\u0930\u0924\u0940\u0924 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 \u091c\u0939\u093e\u0902 \u0921\u0947\u091f\u093e \u092e\u0947\u0902 \u092a\u0948\u091f\u0930\u094d\u0928 x=7 \u0914\u0930 x=10 \u092a\u0930 \u0905\u091a\u093e\u0928\u0915 \u092c\u0926\u0932 \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n
 \u091a\u0930\u0923 2: \u0938\u0930\u0932 \u0930\u0948\u0916\u093f\u0915 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u092e\u0949\u0921\u0932 \u092b\u093f\u091f \u0915\u0930\u0947\u0902<\/strong><\/span><\/h2>\n
 \u0906\u0907\u090f \u092b\u093f\u0930 \u0907\u0938 \u0921\u0947\u091f\u093e \u0938\u0947\u091f \u092e\u0947\u0902 \u090f\u0915 \u0938\u0930\u0932 \u0930\u0948\u0916\u093f\u0915 \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 lm() \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u093e<\/a> \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902 \u0914\u0930 \u0938\u094d\u0915\u0948\u091f\u0930\u092a\u094d\u0932\u0949\u091f \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u0930\u0947\u0916\u093e \u0915\u094b \u092a\u094d\u0932\u0949\u091f \u0915\u0930\u0947\u0902:<\/span> <\/p>\n
 #fit simple linear regression model\n<\/span>linear_fit <- lm(df$y ~ df$x)\n\n#view model summary\n<\/span>summary(linear_fit)\n\nCall:\nlm(formula = df$y ~ df$x)\n\nResiduals:\n    Min 1Q Median 3Q Max \n-5.2143 -1.6327 -0.3534 0.6117 7.8789 \n\nCoefficients:\n            Estimate Std. Error t value Pr(>|t|)    \n(Intercept) 6.5632 1.4643 4.482 0.000288 ***\ndf$x 0.6511 0.1222 5.327 4.6e-05 ***\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 3.152 on 18 degrees of freedom\nMultiple R-squared: 0.6118, Adjusted R-squared: 0.5903 \nF-statistic: 28.37 on 1 and 18 DF, p-value: 4.603e-05\n\n#create scatterplot\n<\/span>plot(df$x, df$y, cex= 1.5<\/span> , pch= 19<\/span> )\n\n#add regression line to scatterplot\n<\/span>abline(linear_fit)<\/strong> <\/pre>\n
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 \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 \u0938\u0930\u0932 \u0930\u0948\u0916\u093f\u0915 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u0930\u0947\u0916\u093e \u0921\u0947\u091f\u093e \u0915\u094b \u0905\u091a\u094d\u091b\u0940 \u0924\u0930\u0939 \u0938\u0947 \u092b\u093f\u091f \u0928\u0939\u0940\u0902 \u0915\u0930\u0924\u0940 \u0939\u0948\u0964<\/span><\/p>\n
 \u0939\u092e \u0907\u0938\u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u0938\u094d\u092a\u0932\u093e\u0907\u0928 \u092e\u0949\u0921\u0932 \u0915\u0947 \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0906\u0930-\u0935\u0930\u094d\u0917 \u092e\u093e\u0928 \u0938\u0947 \u0915\u0930\u0947\u0902\u0917\u0947\u0964<\/span><\/p>\n
 \u091a\u0930\u0923 3: \u0938\u094d\u092a\u094d\u0932\u093e\u0907\u0928 \u0930\u093f\u0917\u094d\u0930\u0947\u0936\u0928 \u092e\u0949\u0921\u0932 \u0915\u094b \u092b\u093f\u091f \u0915\u0930\u0947\u0902<\/strong><\/span><\/h2>\n
 \u0907\u0938\u0915\u0947 \u092c\u093e\u0926, \u0906\u0907\u090f \u0926\u094b \u0928\u094b\u0921\u094d\u0938 \u0915\u0947 \u0938\u093e\u0925 \u090f\u0915 \u0938\u094d\u092a\u0932\u093e\u0907\u0928 \u0930\u093f\u0917\u094d\u0930\u0947\u0936\u0928 \u092e\u0949\u0921\u0932 \u0915\u094b \u092b\u093f\u091f \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0938\u094d\u092a\u094d\u0932\u093f\u0928<\/strong> \u092a\u0948\u0915\u0947\u091c \u0938\u0947 \u092c\u0940\u090f\u0938 ()<\/strong> \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902, \u0914\u0930 \u092b\u093f\u0930 \u0938\u094d\u0915\u0948\u091f\u0930\u092a\u094d\u0932\u0949\u091f \u092a\u0930 \u092b\u093f\u091f \u0915\u093f\u090f \u0917\u090f \u092e\u0949\u0921\u0932 \u0915\u094b \u092a\u094d\u0932\u0949\u091f \u0915\u0930\u0947\u0902:<\/span> <\/p>\n
 library<\/span> (splines)\n\n#fit spline regression model\n<\/span>spline_fit <- lm(df$y ~ bs(df$x, knots=c( 7<\/span> , 10<\/span> )))\n\n#view summary of spline regression model\n<\/span>summary(spline_fit)\n\nCall:\nlm(formula = df$y ~ bs(df$x, knots = c(7, 10)))\n\nResiduals:\n     Min 1Q Median 3Q Max \n-2.84883 -0.94928 0.08675 0.78069 2.61073 \n\nCoefficients:\n                            Estimate Std. Error t value Pr(>|t|)    \n(Intercept) 2.073 1.451 1.429 0.175    \nbs(df$x, knots = c(7, 10))1 2.173 3.247 0.669 0.514    \nbs(df$x, knots = c(7, 10))2 19.737 2.205 8.949 3.63e-07 ***\nbs(df$x, knots = c(7, 10))3 3.256 2.861 1.138 0.274    \nbs(df$x, knots = c(7, 10))4 19.157 2.690 7.121 5.16e-06 ***\nbs(df$x, knots = c(7, 10))5 16.771 1.999 8.391 7.83e-07 ***\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 1.568 on 14 degrees of freedom\nMultiple R-squared: 0.9253, Adjusted R-squared: 0.8987 \nF-statistic: 34.7 on 5 and 14 DF, p-value: 2.081e-07\n\n#calculate predictions using spline regression model\n<\/span>x_lim <- range(df$x)\nx_grid <- seq(x_lim[ 1<\/span> ], x_lim[ 2<\/span> ])\npreds <- predict(spline_fit, newdata=list(x=x_grid))\n\n#create scatter plot with spline regression predictions\n<\/span>plot(df$x, df$y, cex= 1.5<\/span> , pch= 19<\/span> )\nlines(x_grid, preds)<\/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 \u0938\u094d\u092a\u0932\u093e\u0907\u0928 \u0930\u093f\u0917\u094d\u0930\u0947\u0936\u0928 \u092e\u0949\u0921\u0932 \u0921\u0947\u091f\u093e \u0915\u094b \u0915\u093e\u092b\u0940 \u0905\u091a\u094d\u091b\u0940 \u0924\u0930\u0939 \u0938\u0947 \u092b\u093f\u091f \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0938\u0915\u094d\u0937\u092e \u0939\u0948\u0964<\/span><\/p>\n
 \u092e\u0949\u0921\u0932 \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u0938\u0947, \u0939\u092e \u092f\u0939 \u092d\u0940 \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0906\u0930-\u0935\u0930\u094d\u0917 \u092e\u093e\u0928 0.8987<\/strong> \u0939\u0948\u0964<\/span><\/p>\n
 \u0907\u0938 \u092e\u0949\u0921\u0932 \u0915\u0947 \u0932\u093f\u090f \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0906\u0930-\u0935\u0930\u094d\u0917 \u092e\u093e\u0928 \u0938\u0930\u0932 \u0930\u0948\u0916\u093f\u0915 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u092e\u0949\u0921\u0932 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u092e\u0947\u0902 \u092c\u0939\u0941\u0924 \u0905\u0927\u093f\u0915 \u0939\u0948, \u091c\u094b \u0939\u092e\u0947\u0902 \u092c\u0924\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0938\u094d\u092a\u0932\u093e\u0907\u0928 \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u092e\u0949\u0921\u0932 \u0921\u0947\u091f\u093e \u0915\u094b \u092c\u0947\u0939\u0924\u0930 \u0922\u0902\u0917 \u0938\u0947 \u092b\u093f\u091f \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0938\u0915\u094d\u0937\u092e \u0939\u0948\u0964<\/span><\/p>\n
 \u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0902 \u0915\u093f \u0907\u0938 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f \u0939\u092e\u0928\u0947 \u091a\u0941\u0928\u093e \u0939\u0948 \u0915\u093f \u0928\u094b\u0921\u094d\u0938 x=7 \u0914\u0930 x=10 \u092a\u0930 \u0938\u094d\u0925\u093f\u0924 \u0939\u0948\u0902\u0964<\/span><\/p>\n
 \u0935\u094d\u092f\u0935\u0939\u093e\u0930 \u092e\u0947\u0902, \u0906\u092a\u0915\u094b \u0921\u0947\u091f\u093e \u092e\u0947\u0902 \u092a\u0948\u091f\u0930\u094d\u0928 \u0915\u0939\u093e\u0902 \u092c\u0926\u0932\u0924\u0947 \u0926\u093f\u0916\u093e\u0908 \u0926\u0947\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0906\u092a\u0915\u0940 \u0921\u094b\u092e\u0947\u0928 \u0935\u093f\u0936\u0947\u0937\u091c\u094d\u091e\u0924\u093e \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930 \u0938\u094d\u0935\u092f\u0902 \u0928\u094b\u0921 \u0938\u094d\u0925\u093e\u0928 \u091a\u0941\u0928\u0928\u0947 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u094b\u0917\u0940\u0964<\/span><\/p>\n
 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924 \u0938\u0902\u0938\u093e\u0927\u0928<\/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 \u0906\u0930 \u092e\u0947\u0902 \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
 \u0906\u0930 \u092e\u0947\u0902 \u092e\u0932\u094d\u091f\u0940\u092a\u0932 \u0932\u0940\u0928\u093f\u092f\u0930 \u0930\u093f\u0917\u094d\u0930\u0947\u0936\u0928 \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902<\/a>
 \u0906\u0930 \u092e\u0947\u0902 \u0918\u093e\u0924\u0940\u092f \u092a\u094d\u0930\u0924\u093f\u0917\u092e\u0928 \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902<\/a>
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