A personnel officer in a government agency administered four newly developed aptitude tests to each of 25 applications for entry-level clerical positions in the agency. For purpose of the study, all 25 applications 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, X4 ) and the job proficiency score (Y) for the 25 employees were as follows: 1. Obtain the scatter plot matrix. Also obtain the correlation matrix of the X variables. What do the scatter plots suggest about the nature of the functional relationship between the response variable Y and each of the predictor variables? Are any serious multicollinearity problem evident? Explain. 2. Fit the multiple regression function containing all four predictor variables. Does it appear that all predictor variables should be retained? List the all predictor variables that should be retained. 3. Provide the test statistic and associated p-value you would use to test whether Y is dependent on at least one of the predictors. What hypotheses are being tested with the statistic for the question? (Based on question 2) 4. Using stepwise regression, find the best subset of predictor variables to predict job proficiency. (showing it step by step, not using package). What is the R2 value and Interpret R2 in context. 5. Interpret each of the regression coefficients for the model using the stepwise regression. (Based on question 4). 6. Check the assumptions for inference in MLR for the model using the stepwise regression. Do they seem satisfied? Be sure to provide justification. (Based on question 4). 7. Construct a 98% CI for the intercept parameter of your model using the stepwise regression. (using use the values provided in the estimate table) . 8. Construct a 98% CI for the intercept parameter of your model using the stepwise regression. (using the bootstrap method).

the data

Y X1 X2 X3 X4 88.0 86.0 110.0 100.0 87.0 80.0 62.0 97.0 99.0 100.0 96.0 110.0 107.0 103.0 103.0 76.0 101.0 117.0 93.0 95.0 80.0 100.0 101.0 95.0 88.0 73.0 78.0 85.0 95.0 84.0 58.0 120.0 77.0 80.0 74.0 116.0 105.0 122.0 116.0 102.0 104.0 112.0 119.0 106.0 105.0 99.0 120.0 89.0 105.0 97.0 64.0 87.0 81.0 90.0 88.0 126.0 133.0 120.0 113.0 108.0 94.0 140.0 121.0 96.0 89.0 71.0 84.0 113.0 98.0 78.0 111.0 106.0 102.0 109.0 109.0 109.0 109.0 129.0 102.0 108.0 100.0 104.0 83.0 100.0 102.0 127.0 150.0 118.0 107.0 110.0 99.0 98.0 125.0 108.0 95.0 82.0 120.0 94.0 95.0 90.0 67.0 74.0 121.0 91.0 85.0 109.0 96.0 114.0 114.0 103.0 78.0 104.0 73.0 93.0 80.0 115.0 94.0 121.0 115.0 104.0 83.0 91.0 129.0 97.0 83.0