Stat 512 – 1
Solutions to Homework #6
Dr. Levine
1.
In this exercise you will illustrate some of the ideas described in Chapter 7 of the text
related to the extra sums of squares.
Create a new variable called
SAT
which equals
SATM + SATV
and run the following two regressions:
(i)
predict
GPA
using
HSM
,
HSS
, and
HSE
;
Analysis of Variance
Sum of
Mean
Source
DF
Squares
Square
F Value
Pr > F
Model
3
27.71233
9.23744
18.86
<.0001
Error
220
107.75046
0.48977
Corrected Total
223
135.46279
(ii)
predict
GPA
using
SAT
,
HSM
,
HSS
and
HSE
.
Analysis of Variance
Sum of
Mean
Source
DF
Squares
Square
F Value
Pr > F
Model
4
27.88746
6.97187
14.19
<.0001
Error
219
107.57533
0.49121
Corrected Total
223
135.46279
Calculate the extra sum of squares for the comparison of these two analyses. Use it to
construct the F statistic (i.e., general linear test statistic) for testing the null hypothesis that
the coefficient of the
SAT
variable is zero in the model with all four predictors. What are
the degrees of freedom for this test statistic?
Using the SSE definition,
or, using the SSM definition,
The numerator df is (220 – 219) = (4 – 3) = 1.
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, df = (1,219)
Use the
TEST
statement in
PROC REG
to obtain the same test statistic. Give the statistic, degrees of
freedom, P value and conclusion.
Test nosat Results for Dependent Variable gpa
Mean
Source
DF
Square
F Value
Pr > F
Numerator
1
0.17513
0.36
0.5511
Denominator
219
0.49121
F = 0.36, P = 0.5511, do not reject H
0
.
There is no evidence of a linear relationship with SAT
when HSM, HSE, and HSS are in the model.
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 Spring '08
 Staff
 Statistics, Regression Analysis, HSM HSS HSE, Source DF Sum

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