Applied Statistics and Probability for Engineers

Figure S11-4 is a scatter diagram with the transformed variable. This plot appears lin-

ear, indicating that the reciprocal transformation is appropriate. The fitted regression model is

The summary statistics for this model are R^2 0.9800, , andF 0 1128.43

(the Pvalue is 0.0001).

A plot of the residuals from the transformed model versus is shown in Figure S11-5.

This plot does not reveal any serious problem with inequality of variance. The normal proba-

bility plot, shown in Figure S11-6, gives a mild indication that the errors come from a distri-

bution with heavier tails than the normal (notice the slight upward and downward curve at the

extremes). This normal probability plot has the z-score value plotted on the horizontal axis.

Since there is no strong signal of model inadequacy, we conclude that the transformed model

is satisfactory.

Logistic Regression

Linear regression often works very well when the response variable is quantitative.We now

consider the situation where the response variable takes on only two possible values, 0 and 1.

These could be arbitrary assignments resulting from observing a qualitativeresponse. For

yˆ

MSEˆ^2 0.0089

yˆ2.97896.9345 x¿

x¿ (^1) x
11-6
1.0
3.0
0.0 0.10
2.0
DC output,
y
0.20 0.30 0.40 0.50
x' =^1 x
Figure S11-4 Plot of
D C output versus
for the wind-
mill data.
x¿ (^1) x
ei

• 0.4


• 0.6
  0 1


• 0.2

0

0.2

0.4

23

yi

Figure S11-5 Plot of residuals versus

fitted values for the transformed model

for the windmill data.

yˆi

ei

• 0.4


• 0.6
  
  
  • 2 – 1
  
  
  
  


• 0.2

0

0.2

0.4

021

zi

Figure S11-6 Normal probability plot of

the residuals for the transformed model for

the windmill data.

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