Problem 1 (10 marks) File: MALL. XLS A national chain of women's clothing stores with locations in the large shopping malls thinks that it can do a better job of planning more renovations and expansions if it understands what variables impact sales. It plans a small pilot study on stores in 25 different mall locations. The data it collects consist of monthly sales, store size (sq. ft), number of linear feet of window display, number of competitors located in mall, size of the mall (sq. ft),and distance to nearest competitor (ft).

a. Find a multiple regression model for the data.

b. Interpret the values of the coefficients in the model.

c. Test whether the model as a whole is significant. At the 0.05 level of significance, what is your conclusion?

d. Use the model to predict monthly sales for each of the stores in the study.

e. Plot the residuals versus the actual values. Do you think that the model does a good job of predicting monthly sales? Why or why not?

f. Find and interpret the value of ! for this model.

g .Do you think that this model will be useful in helping the planners? Why or why not?

h. Test the individual regression coefficients. At the 0.05 level of significance, what are your conclusions?

i. If you were going to drop just one variable from the model, which one would you choose? Why? The store planners for the women's clothing chain want to find the best model that they can for understanding what store characteristics impact monthly sales.

j. Use stepwise regression to find the best model for the data.

k. Analyze the model you have identified to determine whether it has any problems.

l. Write a memo reporting your findings to your boss. Identify the strengths and weaknesses of the model you have chosen.

Problem 2 (10 marks) The File NFLValues.xlsx show the annual revenue ($ millions) and the estimated team value ($ millions) for the 32 teams in the National Football League.

a. Develop a scatter diagram with Revenue on the horizontal axis and Value on the vertical axis. Does it appear that there are any outliers and/or influential observations in the data?

b. Develop the estimated regression equation that can be used to predict team value given the value of annual revenue.

c. Use residual analysis to determine whether any outliers and/or influential observations are present. Briefly summarize your findings and conclusions.