A company routinely administers an aptitude test to all new management trainees. At the end of the first year with the company, these trainees are graded by their immediate supervisors. The table below shows the results of a regression analysis for a random sample of 12 trainees.The following questions refer to the relationship between the dependent variable "Supervisor's Grade" (Y) and the independent variable "Aptitude Score" (X), which is represented by the linear regression model (i refers to the ith observation or trainee): a)How well does the regression line fit the observed data? Explain. (3 marks)b) What is the sample correlation coefficient between the two variables in this modeland how can it be interpreted? (5 marks)c) Write the sample regression equation clearly defining the variables used.(5 marks)d) Use this equation to estimate the average supervisor's grade of trainees who scored 77 in their aptitude test, and the rate of increase per mark. (7 marks)

+ SUMMARY OUTPUT Regression Statistics Multiple R 0.6001 169 R Square 0.36014029 Adjusted R DO NOT Square 0.29615432 Standard Error 6.48989719 Observations 12 ANOVA Significance df SS MS F F Regression 1 237.0623 237.0623 5.628426 0.039114637 Residual 10 421.1877 42.11877 Total 11 658.25 Standard Upper Coefficients Error t Stat P-value Lower 95% 95% Intercept 43.9161745 13.96597 3.144513 0.01043 12.798 75.0342 Aptitude Score 0.42503334 0.179155 2.37243 0.039115 0.02585 0.82421