{"id":474,"date":"2023-07-29T19:05:27","date_gmt":"2023-07-29T19:05:27","guid":{"rendered":"https:\/\/statorials.org\/ar\/%d8%a7%d9%84%d8%a7%d9%86%d8%ad%d8%af%d8%a7%d8%b1-%d9%85%d8%aa%d8%b9%d8%af%d8%af-%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%b5\/"},"modified":"2023-07-29T19:05:27","modified_gmt":"2023-07-29T19:05:27","slug":"%d8%a7%d9%84%d8%a7%d9%86%d8%ad%d8%af%d8%a7%d8%b1-%d9%85%d8%aa%d8%b9%d8%af%d8%af-%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%b5","status":"publish","type":"post","link":"https:\/\/statorials.org\/ar\/%d8%a7%d9%84%d8%a7%d9%86%d8%ad%d8%af%d8%a7%d8%b1-%d9%85%d8%aa%d8%b9%d8%af%d8%af-%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%b5\/","title":{"rendered":"\u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0645\u062a\u0639\u062f\u062f \u0627\u0644\u062d\u062f\u0648\u062f \u0641\u064a r (\u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629)"},"content":{"rendered":"

<\/p>\n

\n

\u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0645\u062a\u0639\u062f\u062f \u0627\u0644\u062d\u062f\u0648\u062f<\/a> \u0647\u0648 \u0623\u0633\u0644\u0648\u0628 \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647 \u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u062a\u0648\u0642\u0639 \u0648\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629<\/a> \u063a\u064a\u0631 \u062e\u0637\u064a\u0629.<\/span><\/p>\n

\u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u064a\u0623\u062e\u0630 \u0627\u0644\u0634\u0643\u0644:<\/span><\/p>\n

Y = \u03b2 0<\/sub> +<\/sup> \u03b2 1<\/sub> X + \u03b2 2<\/sub> X 2<\/sup> + \u2026 + \u03b2 h<\/sub><\/span><\/p>\n

\u062d\u064a\u062b h<\/em> \u0647\u064a “\u062f\u0631\u062c\u0629” \u0643\u062b\u064a\u0631\u0629 \u0627\u0644\u062d\u062f\u0648\u062f.<\/span><\/p>\n

\u064a\u0648\u0641\u0631 \u0647\u0630\u0627 \u0627\u0644\u0628\u0631\u0646\u0627\u0645\u062c \u0627\u0644\u062a\u0639\u0644\u064a\u0645\u064a \u0645\u062b\u0627\u0644\u0627\u064b \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0644\u0643\u064a\u0641\u064a\u0629 \u062a\u0646\u0641\u064a\u0630 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0645\u062a\u0639\u062f\u062f \u0627\u0644\u062d\u062f\u0648\u062f \u0641\u064a R.<\/span><\/p>\n

\u0627\u0644\u062e\u0637\u0648\u0629 1: \u0625\u0646\u0634\u0627\u0621 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a<\/strong><\/span><\/h3>\n

\u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0633\u0646\u0642\u0648\u0645 \u0628\u0625\u0646\u0634\u0627\u0621 \u0645\u062c\u0645\u0648\u0639\u0629 \u0628\u064a\u0627\u0646\u0627\u062a \u062a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0639\u062f\u062f \u0633\u0627\u0639\u0627\u062a \u0627\u0644\u062f\u0631\u0627\u0633\u0629 \u0648\u062f\u0631\u062c\u0629 \u0627\u0644\u0627\u062e\u062a\u0628\u0627\u0631 \u0627\u0644\u0646\u0647\u0627\u0626\u064a \u0644\u0641\u0626\u0629 \u0645\u0643\u0648\u0646\u0629 \u0645\u0646 50 \u0637\u0627\u0644\u0628\u064b\u0627:<\/span><\/p>\n

 #make this example reproducible<\/span>\nset.seed(1)\n\n#create dataset\n<\/span>df <- data.frame(hours = runif<\/span> (50, 5, 15), score=50)\ndf$score = df$score + df$hours^3\/150 + df$hours* runif<\/span> (50, 1, 2)\n\n#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
 \u0627\u0644\u062e\u0637\u0648\u0629 2: \u062a\u0635\u0648\u0631 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a<\/strong><\/span><\/h3>\n
 \u0642\u0628\u0644 \u0645\u0644\u0627\u0621\u0645\u0629 \u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0644\u0644\u0628\u064a\u0627\u0646\u0627\u062a\u060c \u062f\u0639\u0648\u0646\u0627 \u0623\u0648\u0644\u0627\u064b \u0646\u0646\u0634\u0626 \u0645\u062e\u0637\u0637\u064b\u0627 \u0645\u0628\u0639\u062b\u0631\u064b\u0627 \u0644\u062a\u0635\u0648\u0631 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0633\u0627\u0639\u0627\u062a \u0627\u0644\u062f\u0631\u0627\u0633\u0629 \u0648\u062f\u0631\u062c\u0629 \u0627\u0644\u0627\u0645\u062a\u062d\u0627\u0646:<\/span> <\/p>\n
 library<\/span> (ggplot2)\n\nggplot(df, aes<\/span> (x=hours, y=score)) +\n  geom_point()<\/strong> <\/pre>\n
\"\"<\/p>\n
 \u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u0646 \u0646\u0631\u0649 \u0623\u0646 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0644\u0647\u0627 \u0639\u0644\u0627\u0642\u0629 \u062a\u0631\u0628\u064a\u0639\u064a\u0629 \u0642\u0644\u064a\u0644\u0627\u064b\u060c \u0645\u0645\u0627 \u064a\u0634\u064a\u0631 \u0625\u0644\u0649 \u0623\u0646 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0645\u062a\u0639\u062f\u062f \u0627\u0644\u062d\u062f\u0648\u062f \u0642\u062f \u064a\u0646\u0627\u0633\u0628 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0628\u0634\u0643\u0644 \u0623\u0641\u0636\u0644 \u0645\u0646 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062e\u0637\u064a \u0627\u0644\u0628\u0633\u064a\u0637.<\/span><\/p>\n
 \u0627\u0644\u062e\u0637\u0648\u0629 3: \u062a\u0646\u0627\u0633\u0628 \u0646\u0645\u0627\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0645\u062a\u0639\u062f\u062f \u0627\u0644\u062d\u062f\u0648\u062f<\/span><\/strong><\/h3>\n
 \u0628\u0639\u062f \u0630\u0644\u0643\u060c \u0633\u0646\u0644\u0627\u0626\u0645 \u062e\u0645\u0633\u0629 \u0646\u0645\u0627\u0630\u062c \u0627\u0646\u062d\u062f\u0627\u0631 \u0645\u062a\u0639\u062f\u062f\u0629 \u0627\u0644\u062d\u062f\u0648\u062f \u0645\u062e\u062a\u0644\u0641\u0629 \u0628\u0627\u0644\u062f\u0631\u062c\u0627\u062a h<\/em> = 1…5 \u0648\u0646\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u062a\u062d\u0642\u0642 \u0627\u0644\u0645\u062a\u0642\u0627\u0637\u0639 k-fold \u0645\u0639 k = 10 \u0645\u0631\u0627\u062a \u0644\u062d\u0633\u0627\u0628 \u0627\u062e\u062a\u0628\u0627\u0631 MSE \u0644\u0643\u0644 \u0646\u0645\u0648\u0630\u062c:<\/span><\/p>\n
 #randomly shuffle data\n<\/span>df.shuffled <- df[ sample<\/span> ( nrow<\/span> (df)),]\n\n#define number of folds to use for k-fold cross-validation\n<\/span>K <- 10 \n\n#define degree of polynomials to fit\n<\/span>degree <- 5\n\n#create k equal-sized folds\n<\/span>folds <- cut( seq<\/span> (1, nrow<\/span> (df.shuffled)), breaks=K, labels= FALSE<\/span> )\n\n#create object to hold MSE's of models\n<\/span>mse = matrix(data=NA,nrow=K,ncol=degree)\n\n#Perform K-fold cross validation\n<\/span>for<\/span> (i in<\/span> 1:K){\n    \n#define training and testing data\n<\/span>testIndexes <- which<\/span> (folds==i,arr.ind= TRUE<\/span> )\n    testData <- df.shuffled[testIndexes, ]\n    trainData <- df.shuffled[-testIndexes, ]\n    \n#use k-fold cv to evaluate models\n<\/span>for (j in 1:degree){\n        fit.train = lm<\/span> (score ~ poly<\/span> (hours,d), data=trainData)\n        fit.test = predict<\/span> (fit.train, newdata=testData)\n        mse[i,j] = mean<\/span> ((fit.test-testData$score)^2) \n    }\n}\n\n#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
 \u0648\u0645\u0646 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u0646 \u0646\u0631\u0649 \u0627\u062e\u062a\u0628\u0627\u0631 MSE \u0644\u0643\u0644 \u0646\u0645\u0648\u0630\u062c:<\/span><\/p>\n