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