Download HW 2 - Marriott School

HW 23
Key
24:41
Promotion. These data describe promotional spending by a
pharmaceutical company for a cholesterol-lowering drug. The
data cover 39 consecutive weeks and isolate the area around
Boston. The variables in this collection are shares. Marketing
research often describes the level of promotion in terms of
voice. In place of he level of spending, voice is the share of
advertising devoted to a specific product.
The column Market Share is sales of this product divided by
total sales for such drugs in the Boston area. The column
Detail Voice is the ratio of detailing for this drug to the
amount of detailing for all cholesterol-lowering drugs in
Boston. Detailing counts the number of promotional visits
made by representatives of a pharmaceutical company to
doctors’ offices. Similarly, Sample Voice is the share of
samples in this market that are from this manufacturer.
24:41 a
a. Do any of these
variables have linear
patterns over time? Use
timeplots of each one to
see (scatterplot matrix).
Do any weeks stand out
as unusual?
Week is most linear with
Sample Voice, barely for
Detail Voice, and not
really for Market Share.
24:41 b
b. Fit the multiple regression of Market Share on
three explanatory variables: Detail Voice, Sample
Voice, and Week (which is a simple time trend,
numbering the weeks of the study from 1 to 39).
Does the multiple regression, taken as a whole,
explain statistically significant variation in the
response?
24:41 b
b. The slopes are all not 0. 23% of the variation in
Market Share is explained by the model. F = 4.9
24:41 c
c. Does collinearity affect the estimated effects of
these explanatory variables in the estimated
equation? In particular, do the partial effects
create a different sense of importance from
what is suggested by marginal effects?
The VIFs do not suggest collinearity. The slopes
aren’t even all the same direction.
24:41 c
c. The marginal and partial effects for Sample
Voice and Week are fairly close. Detail Voice is
rather different.
24:41 d
d. Which explanatory variable has the largest VIF?
Sample Voice has the largest VIF, 4.2.
24:41 e
e. What is your substantive interpretation of the
fitted equation? Take into account collinearity
and statistical significance.
There aren’t any real collinearity concerns. To have
a real affect on Market Shares, there needs to be
many visits, but it may not have an actual
impact. Sample voice is the only thing that really
contributes.
24:41 f
f. Should both of the explanatory variables that
are not statistically significant be removed from
the model at the same time? Explain why doing
this would not be such a good idea, in general
(are they collinear?).
Probably not. They may not explain much, but
they are not collinear.
Two insignificant variables might be highly
correlated with each other, but not here.
17:31
Used Cars.
Prices of 155 used BMW. Some have 4 wheel drive
(xi type) and other 2 wheel drive (i type).
17:31 a
a.
17:31 a
a.
17:31 a
a.
17:31 a
a. The two groups
have difference
variances, but this
method does not
require equal
variances. The 95%
CI for the difference
is 618.6 to 2779.3.
The Xi model sells
for about $600 to
$2800 more, on
average.
17:31 b
b. No. The average age of the cars in the two
groups is identical. Age has not confounded the
comparison in “a”.
17:31 b
b.