Please provide detailed calculation and formulas used. Thanks.

A large car dealer evaluates applicants for sale positions on the basis of an aptitude test. The man- agement believes that high scores on the test indicate better potential sales by an applicant. Given below are aptitude test scores of several salesmen and their first month sales on the job (rounded to the nearest thousand dollars). Salesman # 3 4 5 6 8 9 Test Score 51 48 67 72 43 83 60 55 65 Sales 23 25 28 32 28 38 35 26 29 Please answer the following questions (a) Write down the appropriate regression model and its assumptions. (b) Calculate a, y, Sxx, Syy and Sxy. (c) Use the values obtained above to estimate the slope of the SLR model based on ordinary least squares criterion and find the associated standard error. Use these two values to construct a 95% confidence interval for the slope. (d) Test whether the slope is zero or not using an appropriate test at level of significance 0.05. Use p-value approach. - Use rejection region approach. (e) Estimate the intercept of the SLR model based on ordinary least squares criterion. (f) Find the correlation coefficient. (g) Construct a complete regression ANOVA table, state the hypotheses the ANOVA are testing and the corresponding conclusion. (h) Estimate the standard deviation of the random error variable in the SLR model. (i) Find a 90% confidence/prediction(which one) interval for the first month sales volume of a potential salesman who just scored 52 points on the aptitude test. (j) Find a 90% confidence/ prediction (which one) interval for the average first month sales volume of salesmen who just scored 52 points on the aptitude test