This exercise uses Land’s data on tolerance of certain families of pine to salt water flooding given in Table 12.1. For this exercise, replace Hours = 0 with 1 and Y = .00 in Family 3 with .01 to avoid problems with taking logarithms.
(a) Plot Y = chloride content against X = Hours. Summarize what the plot suggests about homogeneous variances, about normality, and about the type of response curve needed if no transformations are made.
(b) Use the plot of the data and the ladder of transformations to suggest a transformation on Y that might straighten the relationship. Suggest a transformation on X that might straighten the relationship. In view of your answer to Part (a), would you prefer the transformation on Y or on X?
(c) Assume a common quadratic relationship of Y (λ) with X for all families, but allow each family to have its own intercept. Use the Box–Cox transformation for λ = 0, .2, .3, .4, .5, .7, and 1.0 and plot the residual sum of squares in each case against λ. At what value of λ does the minimum residual sum of squares occur? Graphically determine 95% confidence limits on λ. What power transformation on Y do you choose?
(d) Repeat Part (c) using a linear relationship between Y (λ) and X. Show how this changes the Box–Cox results and explain (in words) why the results differ.
(e) Use the Box–Cox transformation adopted in Part (c) as the dependent variable. If Y(λ)
is regressed on X using the quadratic model in Part (c), the quadratic term is highly significant. Use the Box–Tidwell method to find a power transformation on X that will straighten the relationship. Plot the residuals from the regression of Y(λ)
on Xα, the Box–Tidwell transformation on X, against
and in a normal plot. Do you detect any problems?
Table 12.1