Statistics Problems

13.2 Observations are taken on sales of a certain mountain bike in 30 sporting goods stores. The regression model was Y = total sales (thousands of dollars), X1 = display floor space (square meters), X2 = competitors’ advertising expenditures (thousands of dollars), X3 = advertised price (dollars per unit). (a) Write the fitted regression equation. (b) Interpret each coefficient. (c) Would the intercept seem to have meaning in this regression? (d) Make a prediction for Sales when FloorSpace = 80, CompetingAds = 100, and Price = 1,200.

Predictor             Coefficient
Intercept                1225
FloorSpace                11.52
CompetingAds          −6.935
Price                         −0.1496

13.4 Refer to the ANOVA table for this regression. (a) State the degrees of freedom for the F test for overall significance. (b) Use Appendix F to look up the critical value of F for α = .05. (c) Calculate the F statistic. Is the regression significant overall? (d) Calculate R2 and R2adj, showing your formulas clearly.

Source                  d.f.            SS                   MS
Regression             3            1,196,410         398,803
Error                     26             379,332            14,590
Total                     29          1,575,742

13.6 Observations are taken on sales of a certain mountain bike in 30 sporting goods stores. Theregression model was Y = total sales (thousands of dollars), X1 = display floor space (square meters), X2 = competitors’ advertising expenditures (thousands of dollars), X3 = advertised price (dollars per unit), X4 = rebate rate (percent of retail price). (a) Calculate the t statistic for each coefficient to test for β = 0. (b) Look up the critical value of Student’s t in Appendix for a two-tailed test at α = .01. Which coefficients differ significantly from zero? (c) Use Excel to find the p-value for each coefficient.

Predictor             Coefficient                   SE
Intercept                     1225.4                     397.3
FloorSpace                     11.522                     1.330
CompetingAds                −6.935                     3.905
Price                               −0.14955                0.08927

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