The following growth data (Y = dry weight in grams) were taken on four independent experimental units at each of six different ages (X = age in weeks). (a) Plot Y versus X. Use the ladder of...

The following growth data (Y = dry weight in grams) were taken on four independent experimental units at each of six different ages (X = age in weeks).

(a) Plot Y versus X. Use the ladder of transformations to determine a power transformation on Y that will straighten the relationship. Determine a power transformation on X that will straighten the relationship. (b) Use the Box–Tidwell method to determine a power transformation on X for the linear model. Does this differ from what you decided using the ladder of transformations? Is there any problem with the behavior of the residuals?

(c) Observe the nature of the dispersion of Y for each level of X. Does there appear to be any problem with respect to the least squares assumption of constant variance? Will either of your transformations in (a) improve the situation? (Do trial transformations on Y for the first, fourth, and sixth levels of X, ages 1, 5, and 9, and observe the change in the dispersion.)