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Mosteller, F. and J. W. Tukey (1977). Data Analysis and Regression: A Second Course in Statistics, Reading,
MA, Addison-Wesley Publishing Co.
Neter, J., W. Wasserman, and M. H. Kutner (1983). Applied Regression Models, Homewood, IL, Richard D.
Irwin Co.
Rawlings, J. O. (1988). Applied Regression Analysis: A Research Tool, Pacific Grove, CA, Wadsworth and
Brooks/Cole.

Exercises

33.1 Model Structure. Are the following models linear or nonlinear in the parameters?
+
(a) η = β 0 β 1 x 2
(b) η = β 0 β 1 2 x
+
+
(c) η = β 0 β 1 x β 2 x + β 3 x + --------------
+
3
2
β 4
x – 60
β 0
(d) η = -----------------
+
x β 1 x
(
(
(e) η = β 0 1 + β 1 x 1 ) 1 + β 2 x 2 )
+
+
+
+
+
+
+
(f) η = β 0 β 1 x 1 β 2 x 2 β 3 x 3 β 12 x 1 x 2 β 13 x 1 x 3 β 23 x 2 x 3 β 123 x 1 x 2 x 3
[
(
(g) η = β 0 1exp – β 1 x)]
–
(
[
(h) η = β 0 1 β 1 exp – x)]
–
(i) ln η() = β 0 β 1 x
+
1
(j) --- = β 0 + β 1
-----
η
x
33.2 Fitting Models. Using the data below, determine the least squares estimates of β and θ by
(
plotting the sum of squares for these models:η 1 = βx 2 and η 2 = 1 – exp θx) .
–
x y 1 y 2
2 2.8 0.44
4 6.2 0.71
6 10.4 0.81
8 17.7 0.93
33.3 Normal Equations. Derive the two normal equations to obtain the least squares estimates of
the parameters in y = β 0 + β 1 x. Solve the simultaneous equations to get expressions for b 0
and b 1 , which estimate the parameters β 0 and β 1 .

© 2002 By CRC Press LLC