1.
KNNL Problem 2.26. To change the axis on a plot, add an “order” statement to the
axis definition.
For example, to make the vertical axis go from 30 to 30 in
increments of 10, do
axis3 label=(angle=90 ‘Residuals’) order=(30 to 30 by 10);
Then use vaxis=axis3 as an option to the plot statement, along with haxis and vref=0.
The mean value of Y appears as Dependent Mean in the output from proc reg.
2.26:
Refer to Plastic hardness Problem 1.22.
(a) Set up the ANOVA table.
Analysis of Variance
Sum of
Mean
Source
DF
Squares
Square
F Value
Pr > F
Model
1
5297.51250
5297.51250
506.51
<.0001
Error
14
146.42500
10.45893
Corrected Total
15
5443.93750
(b)
Test by means of an F test whether or not there is a linear association between
the hardness of the plastic and the elapsed time.
Use a = .01.
State the
alternatives, decision rule, and conclusion.
Testing H
0
:
β
1
= 0 vs H
a
:
β
1
≠
0.
Reject H
0
if Pvalue < 0.01.
Since Pvalue < 0.0001,
we reject H
0
and conclude that there is a significant linear relationship between hardness
and time.
(c)
Plot the deviations
ˆ
i
i
Y
Y

against X
i
on a graph.
Plot the deviations
ˆ
i
Y
Y

against X
i
on another graph, using the same scales as for the first graph.
From
your two graphs, does SSE or SSR (SSM) appear to be the larger component of
SSTO (SST)?
What does this imply about the magnitude of r
2
?
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R e s i
d u a l
s
( O b s e r v e d

P r e d i
c t e d )
 3 0
 2 0
 1 0
0
1 0
2 0
3 0
t i
me
( h o u r s )
1 0
2 0
3 0
4 0
D e v i
a t i
o n s
( P r e d i
c t e d

Me a n )

3 0

2 0

1 0
0
1 0
2 0
3 0
t i
me
( h o u r s )
1 0
2 0
3 0
4 0
On the graphs, it is apparent that the residuals
ˆ
i
i
Y
Y

are much smaller than the
deviations
ˆ
i
Y
Y

of the predictors from the mean.
Thus the SSM should be much larger
than the SSE, and we expect
2
SSM
r
SST
=
to be close to 1.
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 Spring '08
 Staff
 Normal Distribution, Regression Analysis, Standard Deviation, knnl problem, general linear test

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