6. A company's CEO was interested in determining what predictors are linearly related to his employees' job performance (based on a job performance test, it's a score ranging from 0 to 100). Candidate predictors are an employee's IQ score (IQ, a variable with an average of 100 points, ranging from 0 to 200), a social support score (SoSupp, a score indicating the level of social support with a range of 0 to 100), a categorical Motivation variable representing how motivated an employee was (Highly motivated, Average, Not motivated) and Married status (married or not). The following output is some steps from a backward selection regression. In other words, we start from a full model with all 4 potential predictors included in the model. n F P Adj R2 1 BIC I variables I 1 .0126 1. 2. 3. 4. Full - IQ Full - SoSupp Full Full - Married 152 152 152 152 8.626 5.741 24.952 3.597 .0376 .0016 .3702 .0675 .0742 .0439 .0889 25956.78 1 25927.43 1 26156.37 1 24071.24 I variables n F P Adj R2 BIC 1 1 5. Full 6. Fu11 1 Fu11 | Married - IQ 7.153 Married - SoSupp 5.637 Married - Motivation 23.62 .0208 .0412 .0018 .0615 .0702 .0389 25413.28 25668.19 25937.52 1 1 (a) Based on this output, what is the first variable you will remove from the full model? Justify your decision using at most 3 sentences. (b) Write the null and alternate hypotheses being tested in the F-test in the model labeled by 3. Define all variables used. (c) Write out the reduced and full models used in the F test for the model labeled by 5. Define all variables used. (d) Based on the output, what is the next step in the backward selection algorithm? Explain why using at most 5 sentences. 6. A company's CEO was interested in determining what predictors are linearly related to his employees' job performance (based on a job performance test, it's a score ranging from 0 to 100). Candidate predictors are an employee's IQ score (IQ, a variable with an average of 100 points, ranging from 0 to 200), a social support score (SoSupp, a score indicating the level of social support with a range of 0 to 100), a categorical Motivation variable representing how motivated an employee was (Highly motivated, Average, Not motivated) and Married status (married or not). The following output is some steps from a backward selection regression. In other words, we start from a full model with all 4 potential predictors included in the model. n F P Adj R2 1 BIC I variables I 1 .0126 1. 2. 3. 4. Full - IQ Full - SoSupp Full Full - Married 152 152 152 152 8.626 5.741 24.952 3.597 .0376 .0016 .3702 .0675 .0742 .0439 .0889 25956.78 1 25927.43 1 26156.37 1 24071.24 I variables n F P Adj R2 BIC 1 1 5. Full 6. Fu11 1 Fu11 | Married - IQ 7.153 Married - SoSupp 5.637 Married - Motivation 23.62 .0208 .0412 .0018 .0615 .0702 .0389 25413.28 25668.19 25937.52 1 1 (a) Based on this output, what is the first variable you will remove from the full model? Justify your decision using at most 3 sentences. (b) Write the null and alternate hypotheses being tested in the F-test in the model labeled by 3. Define all variables used. (c) Write out the reduced and full models used in the F test for the model labeled by 5. Define all variables used. (d) Based on the output, what is the next step in the backward selection algorithm? Explain why using at most 5 sentences
