assign2-sol - MAR 5621: Advanced Managerial Statistics...

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MAR 5621: Advanced Managerial Statistics Assignment #2 Solutions Grading: Unless otherwise stated, all problems are worth 2 points per letter. 1. The following questions deal with the Magazine data we encountered in Assignment 1 and in class. DV: Page Costs for a 1-page ad IVs: Audience (measured in thousands) Male (percentage of audience that is male) Income (median household income of audience) (a) Which pair of predictors does the best job of predicting PageCosts? Which is a more useful prediction equation: the best single predictor, or the best pair of predictors? Why? (Use a measure that allows for comparing between equations with different numbers of predictors.) Here, we look for the best Adjusted R 2 or lowest residual SD among the 3 models with two predictors in them. The best model with two predictors is the one with Audience and Income. The best two-predictor equation (Audience & Income; Adj R 2 =.7754) does a little bit better job than the best one-predictor equation (Audience only; Adj R 2 =.7564), even after adjusting for its larger number of predictors. Another way to address this is by testing whether Income is a significant predictor in the Audience and Income model (which it is, p=.02297 from the detailed output (b) (3 pts) If you knew the Audience score for a magazine, would it be helpful for you to know the Income score for that magazine also? Explain why or why not. Test the null hypothesis that, holding Audience constant, Income is unrelated to PageCosts. Report an appropriate p-value, and state your conclusion of the hypothesis test in a simple English sentence. Part (a) dealt with this same issue. By comparing Adjusted R 2 we found that the Audience & Income model is indeed better than the Audience only model. So it is useful to know Income in addition to Audience. Based on the fact that the Audience & Income model fits better than the Audience- only model, we expect the Income coefficient to not be zero. We can verify this by Using the regression output for the Audience & Income model: The Income coefficient is .718 with a standard error of .306, producing a t-statistic of 2.34 and a p-value of .023. Using the usual significance level of .05, we reject the null hypothesis that the slope for Income is 0. Conclusion: Holding Audience constant, Income is positively related to PageCosts.
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(c) Compare the coefficient for Income in the Income-only model, and in the Audience & Income model. Why is it different? Why does the sign change? Explain, in as simple English as possible. Income is a significant predictor in the Income & Audience model, but is not a significant predictor in the Income-only model. Here, the Income coefficient changes from negative and nonsignificant (b= -0.74, p=.22) to positive and significant (b=0.72, p=.023) when Audience is added to the model. The coefficient changes because Income and Audience are correlated.
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assign2-sol - MAR 5621: Advanced Managerial Statistics...

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