Q6 A personnel officer in a governmental agency administered two newly developed aptitude tests to a random sample of 13 applicants for entry-level positions in the agency. For the purpose of the study, all 13 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 two tests (x1, x2) and the job proficiency score (y) for the 13 employees are in the following: Job Aptitude Aptitude proficiency test 1 test 2 score (y) score (x1) score (x2) 88 110 100 80 97 99 96 107 103 76 117 93 80 101 95 73 85 95 58 77 80 116 122 116 104 119 106 99 89 105 64 81 90 126 120 113 94 121 96a i) Fit a regression line using job proficiency score as Y and aptitude test 1 score as X. Use calculator to find the a and b to do so. ii) Find the coefficient of correlation in this regression model. Interpret its meaning. iii) Find the coefficient of determination in this regression model. Interpret its meaning.b) Now the personnel officer wants to include one more variable, aptitude test 2 score, in the regression model. Thus he obtains the following Excel output using both aptitude test 1 score and aptitude test 2 score as independent variables: SUMMARY OUTPUT Regression Statistics Multiple R 0.95899685 R Square 0.91967496 Adjusted R Square Standard Error 6.12488914 Observations 13 ANOVA df SS MS F Significance F Regression 2 4295.165022 Residual 10 375.1426698 Tota 12 4670.307692 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 102.05967 18.41703463 Aptitude test 1 score (x1) 0.26091492 0.144093118 Aptitude test 2 score (x2) 1.64956174 0.245511906 i) From the Excel output, fit a regression model using aptitude test 1 score as X1 and aptitude test 2 score as X2. ii) Interpret the coefficient of X1 and X2. iii) Calculate the adjusted R square for this regression model. iv) Test the overall significance of this regression model at a = 0.05 v) Test the significance of X1 (aptitude test 1 score) and X2 (aptitude test 2 score) individually in the regression model at a = 0.05 vi) Estimate the job proficiency score with aptitude test 1 score is 111 marks and aptitude test 2 score is 97 marks.0) Comparing regression model in (a) and (b), which regression model should be used by the researcher