Note that we could have recalculated the weights but the difference would not be much and
the question specified to use the weights from part (b).
PROC REG Data=ChromaOut plots=none;
Model LogOut=Amt1 Amt5 Amt20;
Weight w;
Plot Student.*Predicted.;
Plot Student.*nqq.;
run;
Weight: w
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square
F Value
Pr > F
Model
3
1245.56987
415.18996
68612.8
<.0001
Error
16
0.09682
0.00605
Corrected Total
19
1245.66669
Root MSE
0.07779
R-Square
0.9999
Dependent Mean
5.43278
Adj R-Sq
0.9999
Coeff Var
1.43185
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard
Error
t Value
Pr > |t|
Intercept
1
1.95207
0.05182
37.67
<.0001
Amt1
1
1.43833
0.05216
27.58
<.0001
Amt5
1
3.39010
0.05256
64.50
<.0001
Amt20
1
4.87291
0.05204
93.64
<.0001

[4 marks]
We note that the parameter estimates are exactly the same in the weighted and unweighted
analysis but the standard errors are quite different. The weighted mean squared error is larger
than in the unweighted case and so the standard errors in the weighted regression are larger.
The
R
2
in the weighted regression is almost 100% slightly better than in the unweighted
regression. Most importantly, the diagnostic plots for the weighted regression suggest that the
variability is now constant and the linearity assumption does not seem violated. There may
still be some question about the normality but the weighted studentized residuals are closer
to normal than the unweighted.
[3 marks]

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