Department of Statistics
The Wharton School
University of Pennsylvania
Statistics 621
Fall 2008
Solutions, Final Exam
(1)
(2)
Assuming the MRM holds, if the 95% confidence interval for the intercept
β
0
in a
multiple regression model is the interval [-18, 54], then
the standard error of the
estimated intercept is about 18.
The length of the 95% confidence interval is approximately 4 times the SE. Since
the interval includes zero, the estimate is not statistically significantly different from
zero.
(3)
The intercept is often an extrapolation in a regression model because
zero lies outside
the range of the explanatory variables.
An extrapolation occurs when the value used for the explanatory variable lies
outside the range of the data.
This often occurs for the intercept since the intercept is
the fitted value when
x
= 0.
(4)
A narrow cluster of observations at the center of the leverage plot of an explanatory
variable in a multiple regression suggests that
this variable is collinear with other
explanatory variables
.
The position of points on the horizontal axis of the leverage plot is determined by
the variation in the variable that remains after removing the effects of other
explanatory variables. In the presence of high correlation among the X’s, there’s little
such variation left.
(5)
In order to build a regression model that estimates a constant marginal elasticity of
sales with respect to price, we must
fit a simple regression of log sales on log price
.
The slope in a log-log model is the elasticity.
(6)
The explanatory variables in a multiple regression are assumed by the multiple
regression model to
be linearly related to the response
.
Normality is only assumed
about the error variation.
The values of the explanatory variable are set by the
experimenter and not part of the assumptions of the model.
(7)
The overall
F
-ratio in a multiple regression with
K
explanatory variables (found in the
analysis of variance table
) tests
H
0
:
β
1
=
β
2
= … =
β
K
= 0
.
This is the overall F-test
of the entire model, measuring whether
R
2
is larger than could be expected from
unrelated variables.
(8)
To check for the presence of heteroscedasticity in a multiple regression model, it is
recommended that we
plot the residuals of the model versus the fitted values
.
Heteroscedasticity often occurs as the predicted values get larger; this plot shows the
data in order of increasing predicted values.

Statistics 621, Solutions to the Final Exam
-2-
Q1, 2008
(9)
In order to allow the effect of the explanatory variable
Advertising
(which measures
promotional spending) on the response
Sales
(which measures retail sales at various
stores) to depend upon the geographic
Location
of the stores (a categorical variable),
we should
include
Location
and its interaction with
Advertising
in our model
.

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