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 1page 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 twopredictor equation (Audience & Income; Adj R
2
=.7754) does a little bit
better job than the best onepredictor 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
for the Audience & Income model )
(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 pvalue, 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
looking at the output for the Audience & Income model.
Using the regression output for the Audience & Income model:
The Income
coefficient is .718 with a standard error of .306, producing a tstatistic of 2.34 and a
pvalue 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 Incomeonly 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 Incomeonly 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.
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 Spring '09
 Regression Analysis, R Square, SATSUM

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