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Section Exercise 13-8 Refer to the ANOVA table for this regression. Source 55 d. f . MS Regression 1, 182, 733 4 295, 683 Residual 1, 584, 952 45 35, 221 Total 2, 767, 685 49 Click here for the Excel Data File (a) State the degrees of freedom for the Ftest for overall significance. The degrees of freedom for regression are and for error (b) Use Appendix F to look up the critical value of Ffor a= .05. (Round your answer to 2 decimal places.) F.05 (c-1) Calculate the Fstatistic. (Round your answer to 4 decimal places.) F statistic (c-2) The overall regression is significant. O Yes O No (c-3) The hypotheses is a. He: All the coefficients are zero (B1 = B2 = 3 = 0) vs. Hy: At least one coefficient is not zero. b. He: At least one coefficient is non-zero vs. Hy: All the coefficients are zero (B1 = B2 = B3 = 0) O a Ob(d) Calculate Re and R2 adj. (Round your answers to 4 decimal places.) R2 R-adjSection Exercise 13-10 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). Click here for the Excel Data File (a) Fill in the values in the table given here. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "O" wherever required. Round your t-values to 3 decimal places and p-values to 4 decimal places.) Predictor Coefficient SE tcalc p-value Intercept 1, 225.4 397.3 FloorSpace 11.522 1.330 Competing Ads -6.935 3.905 Price -0. 14955 0. 08927 (b-1) What is the critical value of Student's tin Appendix D for a two-tailed test at a = .01? (Round your answer to 3 decimal places.) t-value = (b-2) Choose the correct option. O Only CompetingAds differs significantly from zero. O Only Price differs significantly from zero. O Only FloorSpace differs significantly from zero.Chapter Exercise 13-50 Using test data on 43 vehicles, an analyst fitted a regression to predict CityMPG (miles per gallon in city driving) using as predictors Length (length of car in inches), Width (width of car in inches), and Weight (weight of car in pounds). R2 0. 682 Adjusted R2 0. 658 n 43 R 0. 826 k 3 Std. Error 2.558 Dep. Var. CityMPG ANOVA table Source 55 of MS F p-value Regression 547 . 3722 W 182.4574 27.90 8. 35E-10 Residual 255. 0929 39 6.5408 802. 4651 42 Regression output confidence interval variables Coefficients Std. Error t Stat p-Value Lower 95% Upper 95% VIF Intercept 39 .4492 8.1678 4.830 0. 0900 22.9283 55.9701 Length (in) -0. 0916 0. 0454 -0.035 0.9725 -0. 0934 0. 0902 2.669 Width (in) -0.0463 0. 1373 -0.337 0.7379 -0.3239 0 . 2314 2.552 Weight (1bs) -0. 9043 0. 0908 -5.166 0. 0900 -0. 0960 -0. 0026 2.836 (a) Referring to the Fstatistic and its p-value, what do you conclude about the overall fit of this model? The regression is (Click to select) v based on the Fcalc and p-value(b) Do you see evidence that some predictors were unhelpful? (You may select more than one answer. Single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box fo a wrong answer.) ? Length ? Width ? Weight (c) Do you suspect that multi-colllinearity is a problem? O Yes O NoSection Exercise 13-16 A regression model to predict the price of diamonds included the following predictor variables: the weight of the stone (in carats where 1 carat = 0.2 gram), the color rating (D, E, F, G, H, or 1), and the clarity rating (IF, VVS1, VVS2, VS1, or VS2). (a) Identify the quantitative predictor variable(s). (You may select more than one answer. Click the box with a check mark for the correct answer and double click to empty the box for the wrong answer.) ? Weight ? Color Rating ? Clarity Rating (b) How many indicator variables would be included in the model in order to prevent the least squares estimation from failing? Indicator Variables (c) Choose the correct model form for predicting diamond price. a. Price = Be + B1 Weight + B2 ColorD + B; ColorE + BA ColorF + Bs ColorG + BE ColorH + B, ClarityIF + Bg ClarityVVS1+ Bg ClarityVVS2+ Bio ClarityVS1 b. Price = Be + B1 Weight + B2 Color + B3 Clarity c. Price = Be + B, Weight + B2 ColorD + B3 ColorE + BAColorF + Bs ColorG + BE ColorH + B, Colori+ Bg ClarityIF + Bg ClarityVVS1+ Bio ClarityVVS2+ B11 ClarityVS1+$12 ClarityVS1 O a Ob
