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.
(a)
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,
(
)
(
)
(
)
(
)

,
,
,
,
,
,
,
107.75046
107.57533
0.17513
SSM
sat
hsm hss hse
SSE hsm hss hse
SSE sat hsm hss hse
=
−
=
−
=
or, using the SSM definition,
(
)
(
)
(
)
(
)

,
,
,
,
,
,
,
27.88746
27.71223
0.17513
SSM
sat
hsm hss hse
SSM
sat hsm hss hse
SSM
hsm hss hse
=
−
=
−
=
The numerator df is (220 – 219) = (4 – 3) = 1.
(
) ( )
(
)

,
,
/ 1
0.17513/1
0.35653
0.49121
SSM
sat
hsm hss hse
F
MSE
full
=
=
=
, df = (1,219)
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