Questions 1 and 2 are based on Sections 14.4 -14.5 Model assumption and testing.

1. A Regression analysis was applied between sales data (y in $1000s) and advertising expenditure (x in $100s) and the estimated regression equation is obtained as ŷ = 12 + 1.8x.

Suppose SST = 300,SSE = 75, sb1 = 0.2683 and n = 17

a) Carry out a t-test to see whether the advertising expenditure is significant. Use α = 0.05 and critical value approach to draw your conclusion. Make sure to show all your steps.

b) Carry out an F-test to see whether the advertising expenditure is significant. Use α = 0.05 and critical value approach to draw your conclusion. Make sure to show all your steps.

2. A sales manager collected data on annual sales for new customer accounts and the number of years of experience for a sample of 15 salespersons. The following is the Regression Analysis run by Minitab for developing an estimated regression equation to predict annual sales using the independent variable years of experience

(x). Note that x = years of experience, y = annual sales.

Regression Analysis: Annual Sales versus Years of Experience

Regression Equation

Annual Sales = 53.86 + 8.361 Years of Experience

a) Carry out a t-test to see whether the years of experience and the annual sales are related. Use α = 0.05. Please use the P-value approach to answer this question.

b) Carry out an F-test to see whether years of experience and the annual sales are related. Use α = 0.05. Please use the P-value approach to answer this question.

c) Find a 95% confidence interval for the mean annual sales for all salespersons with nine years of experience.

d) The company is considering hiring Tom Smart, a salesperson with nine years of experience. Find a 95% prediction interval of annual sales for Tom Smart.

e) Discuss the differences in your answers to part c) and d). That is, which interval estimation is wider? And why?

Questions 3 is based on Sections 14.8 -14.9 Residual analysis.

3. The following data were used to develop a regression analysis.

a) The graph shown below is the residual against the fitted value (ŷ) to check the constant variance assumption.

Does the above plot support the assumptions about the error E? Explain.

b) The graph shown below is the normal probability to check the normality assumptions about the error E.

Does the above plot support the assumptions about the error E? Explain.

c. The following results are part of the Regression Analysis for the above data from Minitab. Below is a table with statistics necessary for analyzing the residuals.

SRES stands for standardized residual and HI for leverage values. 

Questions 4 is based on Sections from chapter 15.

4. This question is from the textbook: Problem 25 on Page 705.

The Minitab output for this question is given below.

Regression Analysis: Overall versus Itineraries/Schedule, Shore Excursions, Food/Dining

Please answer ONLY for parts of a, b, c (Do not answer for part d) and the following part e and f.

e. Provide a 95% confidence interval for the mean value for all ships that got Itineraries/Schedule score 90, Shore Excursions score 80 and Rood/Dining score 88.

f. Provide a 95% prediction interval for the mean value for one specific ship that got Itineraries/Schedule score 90, Shore Excursions score 80 and Rood/Dining score 88.