Dataset: JobProf.txt Y,X1,X2,X3,X4 88,86,110,100,87 80,62,97,99,100 96,110,107,103,103 76,101,117,93,95 80,100,101,95,88 73,78,85,95,84 58,120,77,80,74 116,105,122,116,102 104,112,119,106,105 99,120,89,105,97 64,87,81,90,88 126,133,120,113,108 94,140,121,96,89 71,84,113,98,78 111,106,102,109,109 109,109,129,102,108 100,104,83,100,102 127,150,118,107,110 99,98,125,108,95 82,120,94,95,90 67,74,121,91,85 109,96,114,114,103 78,104,73,93,80 115,94,121,115,104 83,91,129,97,83

Please Use R for a solution.

A personnel officer in a governmental agency administered four newly developed aptitude tests to each of 25 applicants for entry-level clerical positions in the agency. For purpose of the study, all 25 applicants were accepted for positions irrespective of their test scores. After a probationary period, each applicant was rated for proficiency on the job. The scores on the four tests (X1, X2, X3, X ) and the job proficiency score (Y) for the 25 employees were in the data file "JobProf.txt" (a) Fit the regression model containing all four predictor variables as first-order terms. Show the table of the fitted model: coefficients estimation, their standard deviation, 2-score, and p-values. What is the estimation 2? Does it appear that all predictor variables should be retained? Use significant level a = 0.05. (b) Use the best-subset and Cp criterion. Write down the best sub-model and its corresponding Cp value. (c) Use forward and backward variable selection (AIC as criterion) to find the optimal sub-model. Do they return the same optimal sub-model? Write down the optimal model(s) returned by the two methods, and compare the model(s) with the model in (a) using F-test. (a = 0.05) (a) Use the lasso and least angle regression method to fit the model containing all four predictors. Re- turn the two profiles of lesso and lar coefficients. (Use the 'plot' function.) Are there any difference between the two profiles? A personnel officer in a governmental agency administered four newly developed aptitude tests to each of 25 applicants for entry-level clerical positions in the agency. For purpose of the study, all 25 applicants were accepted for positions irrespective of their test scores. After a probationary period, each applicant was rated for proficiency on the job. The scores on the four tests (X1, X2, X3, X ) and the job proficiency score (Y) for the 25 employees were in the data file "JobProf.txt" (a) Fit the regression model containing all four predictor variables as first-order terms. Show the table of the fitted model: coefficients estimation, their standard deviation, 2-score, and p-values. What is the estimation 2? Does it appear that all predictor variables should be retained? Use significant level a = 0.05. (b) Use the best-subset and Cp criterion. Write down the best sub-model and its corresponding Cp value. (c) Use forward and backward variable selection (AIC as criterion) to find the optimal sub-model. Do they return the same optimal sub-model? Write down the optimal model(s) returned by the two methods, and compare the model(s) with the model in (a) using F-test. (a = 0.05) (a) Use the lasso and least angle regression method to fit the model containing all four predictors. Re- turn the two profiles of lesso and lar coefficients. (Use the 'plot' function.) Are there any difference between the two profiles