Question: Consider the data in Table. Use the X values from that table, but let Y be defined as Y = 4 + 3X1.7. Then plot Y against X and notice the nonlinearity. What should be the value of the residual sum of squares if use of the Box-Tidwell procedure permits identification of the correct model? Use five iterations of the Minitab macro BOXTID described in the chapter appendix to determine the transformation that is suggested by application of the Box-Tidwell procedure. What is the (approximate) value of a to which the procedure appears to be converging? What is the value of the residual sum of squares when that value of a is used? Will use of the Box-Tidwell procedure identify the need for a nonlinear term in addition to the linear term, or will it identify the nonlinear term that would be used without a linear term? How could the procedure be modified to detect the need for a nonlinear term in addition to the linear term?
Compute the correlation between X and X1.7. Then consider the value of R2 and comment on the Mosteller-Tukey rough rule-of-thumb regarding the apparent need for a transformation of these data.
Y X
10 5
11 10
16 8
18 13
25 15
24 18
26 22
29 21
31 19
31 26
34 25
35 29
36 28