Applied Statistics and Probability for Engineers

respect. However, it is always possible to fit a polynomial of degree n1 to ndata points,

and the experimenter should not consider using a model that is “saturated”—that is, that has

very nearly as many independent variables as observations on y.

11-10 MORE ABOUT TRANSFORMATIONS (CD ONLY)

An Example

As noted earlier in Section 11-9, transformations can be very useful in many situations where

the true relationship between the response Yand the regressor xis not well approximated by a

straight line. The utility of a transformation is illustrated in the following example.

EXAMPLE S11-2 A research engineer is investigating the use of a windmill to generate electricity and has col-

lected data on the DC output from this windmill and the corresponding wind velocity. The

data are plotted in Figure S11-2 and listed in Table S11-2.

Inspection of the scatter diagram indicates that the relationship between DC output Yand

wind velocity (x) may be nonlinear. However, we initially fit a straight-line model to the data.

The regression model is

yˆ0.13090.2411 x

11-4

1.0

0 2

2.0

3.0

0.0

DC output,

y

4 6 8 10

Wind velocity, x

Figure S11-2 Plot of

DC output yversus

wind velocity xfor the

windmill data.

0.4

0.2

0.0

• 0.2


• 0.4


• 0.6
  0.4

ei

0.8 1.2 1.6 2.0 2.4

y

Figure S11-3 Plot of

residuals eiversus fit-

ted values for the

windmill data.

yˆi

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