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Marketing Homework Help Regression Analysis QUESTION 1 Please look at the following output from the regression. What does the value of R-square tell us about our model? Note: It is not sufficient to just provide some general answers. Use the numbers from the output, and write your answers specific to our regression model. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .771a .594 .580 21.741 a. Predictors: (Constant), DENSITY Path: pWords:0 12.5 points Save Answer QUESTION 2 Please look at the following output from the regression. What do the value of F-test and its P-value tell us about our model? Note: It is not sufficient to just provide some general answers. Use the numbers from the output, and write your answers specific to our regression model. ANOVAa Model Sum of Squares df Mean Square F Sig. 1 Regression 20747.246 1 20747.246 43.895 .000b Residual 14179.629 30 472.654 Total 34926.875 31 a. Dependent Variable: SALES b. Predictors: (Constant), DENSITY Path: pWords:0 12.5 points Save Answer QUESTION 3 The regression coefficient output is shown below. Does Density matter in terms of explaining sales? Can you provide an explanation of the coefficient estimate for Density? (Note: the unit of Density is number of homes per acre, and the unit of Sales is dollars per thousand homes ). Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 141.525 9.109 15.538 .000 DENSITY -12.893 1.946 -.771 -6.625 .000 a. Dependent Variable: SALES For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). 5 Path: pWords:28 12.5 points Saved QUESTION 4 Managers suspect that the effect of Density on Sales can be nonlinear; in other words, as density increases, there will a decreasing marginal effect on density. To test this idea, they ran an additional regression, with Density and Density_Squared (i.e. Density*Density) as the independent variables (again, Sales as the dependant variable), and the output of the new regression shows below. Can you explain what the R_square and F-test tell us about the new model? Is the new model better than the model with only Density as the independent variable? Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .910a .829 .817 14.354 a. Predictors: (Constant), Density2, DENSITY ANOVAa Model Sum of Squares df Mean Square F Sig. 1 Regression 28951.384 2 14475.692 70.253 .000b Residual 5975.491 29 206.051 Total 34926.875 31 a. Dependent Variable: SALES b. Predictors: (Constant), Density2, DENSITY Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 212.595 12.768 16.650 .000 DENSITY -47.293 5.601 -2.827 -8.444 .000 Density2 3.419 .542 2.113 6.310 .000 a. Dependent Variable: SALES Path: pWords:0 12.5 points Save Answer QUESTION 5 (This is a Bonus Question) Continuing from Question 4, can you explain the meaning of the coefficient estimate of Density_Squared (i.e. Density*Density)? (Hint: the effect of Density on Sales is negative, while the effect of Density_Squared on Sales is positive).
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