9.9Polynomial Regression 393
might hold. Since
∑
i
xi=55,
∑
i
xi^2 =385,
∑
i
xi^3 =3,025,
∑
i
xi^4 =25, 333
∑
i
Yi=1,291.1,
∑
i
xiYi=9,549.3,
∑
i
xi^2 Yi=77,758.9
the least squares estimates are the solution of the following set of equations.
1,291.1= 10 B 0 + 55 B 1 + 385 B 2 (9.9.1)
9,549.3= 55 B 0 + 385 B 1 +3,025B 2
77,758.9= 385 B 0 +3,025B 1 +25,333B 2
Solving these equations (see the remark following this example) yields that the least
squares estimates are
B 0 =12.59326, B 1 =6.326172, B 2 =2.122818
Thus, the estimated quadratic regression equation is
Y=12.59+6.33x+2.12x^2
This equation, along with the data, is plotted in Figure 9.14. ■
300
250
200
150
100
50
0
Y
246810
x
FIGURE 9.14