A researcher was investigating possible explanations for deaths in traffic accidents.
He
examined data from 1991 for each of the 50 states plus the District of Columbia.
The data
included the number of deaths in traffic accidents (labeled as the variable Deaths), the average
income per family (labeled as the variable Income), and the number of children (in multiples of
100,000) between the ages of 1 and 14 in the state (labeled as the variable Children).
As part of
his investigation he ran the following multiple regression model
Deaths =
E
0
+
E
1
(Children) +
E
2
(Income) +
H
i
where the deviations
H
i
were assumed to be independent and normally distributed with mean 0
and standard deviation
V
.
This model was fit to the data using the method of least squares.
The
following results were obtained from statistical software.
Source
df
Sum of Squares
Model
2
48362278
Error
48
3042063
Variable
Parameter Est.
Standard Error of Parameter Est.
Constant
593.829
204.114
Children
90.629
3.305
Income
–0.039
0.015
1.
The value of the regression standard error is
A) 0.015.
B) 3.305.
C) 204.14.
D) 251.74.
2.
Suppose we wish to test the hypotheses
H
0
:
E
1
=
E
2
= 0,
H
a
: at least one of the
E
j
is not 0
using the ANOVA
F
test.
The
P
value of the test is
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3.
A 99% confidence interval for
E
2
, the coefficient of the variable Income, is
4.
The proportion of the variation in the variable Deaths that is explained by the
explanatory variables Children and Income is
5.
Based on the above analyses, we conclude
A)
the variable Income is statistically significant at level 0.05 as a predictor of the variable
Deaths.
B)
the variable Income is statistically significant at level 0.05 as a predictor of the variable
Deaths in a multiple regression model that includes the variable Children.
C)
the variable Income is not useful as a predictor of the variable Deaths and should be
omitted from the analysis.
D)
the variable Children is not useful as a predictor of the variable Deaths, unless the
variable Income is also present in the multiple regression model.
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 Spring '08
 STAFF
 Regression Analysis, researcher, multiple regression model

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