Introduction to Probability and Statistics for Engineers and Scientists

392 Chapter 9: Regression

Even more so than in linear regression, it is extremely risky to use a polynomial fit to
predict the value of a response at an input levelx 0 that is far away from the input levels
xi,i=1,...,nused in finding the polynomial fit. (For one thing, the polynomial fit
may be valid only in a region around thexi,i=1,...,nand not includingx 0 .)

EXAMPLE 9.9a Fit a polynomial to the following data.

xY

1 20.6

2 30.8

355

4 71.4

597.3

6 131.8

7 156.3

8 197.3

9 238.7

10 291.7

SOLUTION A plot of these data (see Figure 9.13) indicates that a quadratic relationship

Y=β 0 +β 1 x+β 2 x^2 +e

300

250

200

150

100

50

0

Y

246810

x

FIGURE 9.13