1. To ensure a successful test marketing of its OmniPower energy bars, the OmniFoods marketing department has contracted with In-Store Placements Group (ISPG), a merchandising consultancy. ISPG will work with the grocery store chain that is conducting the test-market study. Using the same 34-store sample used in the test-market study, ISPG claims that the choice of shelf location and the presence of in-store OmniPower coupon dispensers both increase sales of the energy bars. Open Omni_ISPGMemo.pdf to review the ISPG claims and supporting data.

Then answer the following questions:

a. Are the supporting data consistent with ISPGs claims? Perform an appropriate statistical analysis to confirm (or discredit) the stated relationship between sales and the two independent variables of product shelf location and the presence of in- store OmniPower coupon dispensers.

b. If you were advising OmniFoods, would you recommend using a specific shelf location and in-store coupon dispensers to sell OmniPower bars?

c. What additional data would you advise collecting in order to determine the effectiveness of the sales promotion techniques used by ISPG?

2. Measuring the height of a California redwood tree is a very difficult undertaking because these trees grow to heights of over 300 feet. People familiar with these trees understand that the height of a California redwood tree is related to other characteristics of the tree, including the diameter of the tree at the breast height of a person. The data in represent the height (in feet) and diameter (in inches) at the breast height of a person for a sample of 21 California redwood trees.

a. Assuming a linear relationship, use the least-squares method to compute the regression coefficients b 0 and b 1. State the regression equation that predicts the height of a tree based on the trees diameter at breast height of a person.

b. Interpret the meaning of the slope in this equation.

c. Predict the height for a tree that has a breast height diameter of 25 inches.

d. Interpret the meaning of the coefficient of determination in this problem.

e. Perform a residual analysis on the results and determine the adequacy of the model.

f. Determine whether there is a significant relationship between the height of redwood trees and the breast height diameter at the 0.05 level of significance.

g. Construct a 95% confidence interval estimate of the population slope between the height of the redwood trees and breast height diameter.

3. Leasing agents from the Triangle Mall Management Corporation have suggested that Sunflowers consider several locations in some of Triangles newly renovated lifestyle malls that cater to shoppers with higher-than-mean disposable income. Although the locations are smaller than the typical Sunflowers location, the leasing agents argue that higher-than-mean disposable income in the surrounding community is a better predictor than store size of higher sales. The leasing agents maintain that sample data from 14 Sunflowers stores prove that this is true.

Open Triangle_Sunflower.pdf and review the leasing agents proposal and supporting documents.

Then answer the following questions:

a. Should mean disposable income be used to predict sales based on the sample of 14 Sunflowers stores?

b. Should the management of Sunflowers accept the claims of Triangles leasing agents? Why or why not?

c. Is it possible that the mean disposable income of the surrounding area is not an important factor in leasing new locations? Explain.

d. Are there any other factors not mentioned by the leasing agents that might be relevant to the store leasing decision?

4. Professional basketball has truly become a sport that generates interest among fans around the world. More and more players come from outside the United States to play in the National Basketball Association (NBA). You want to develop a regression model to predict the number of wins achieved by each NBA team, based on field goal (shots made) percentage for the team and for the opponent. The data are stored in NBA2011.xls.

a. State the multiple regression equation.

b. Interpret the meaning of the slopes in this equation.

c. Predict the number of wins for a team that has a field goal percentage of 45% and an opponent field goal percentage of 44%.

d. Perform a residual analysis on your results and determine whether the regression assumptions are valid.

e. Is there a significant relationship between number of wins and the two independent variables (field goal percentage for the team and for the opponent) at the 0.05 level of significance?

f. Determine the p-value in (e) and interpret its meaning.

g. Interpret the meaning of the coefficient of multiple determination in this problem.

h. Determine the adjusted r²

i. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the most appropriate regression model for this set of data.

j. Determine the p-values in (i) and interpret their meaning.

5. A sample of 30 recently sold single-family houses in a small city is selected. Develop a model to predict the selling price (in thousands of dollars), using the assessed value (in thousands of dollars) as well as time (in months since reassessment). The houses in the city had been reassessed at full value one year prior to the study. The results are stored in House1.xls.

a. State the multiple regression equation.

b. Interpret the meaning of the slopes in this equation.

c. Predict the selling price for a house that has an assessed value of $170,000 and was sold 12 months after reassessment.

d. Perform a residual analysis on your results and deter-mine whether the regression assumptions are valid.

e. Determine whether there is a significant relationship be-tween selling price and the two independent variables (assessed value and time period) at the 0.05 level of significance.

f. Determine the p-value in (e) and interpret its meaning.

g. Interpret the meaning of the coefficient of multiple determination in this problem.

h. Determine the adjusted

i. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the most appropriate regression model for this set of data.

j. Determine the p-values in (i) and interpret their meaning.

k. Construct a 95% confidence interval estimate of the population slope between