The data in the accompanying table were taken to develop standardized soil moisture curves for each of six soil types. Percent soil moisture is determined at each of six pressures. The objective is to...

The data in the accompanying table were taken to develop standardized soil moisture curves for each of six soil types. Percent soil moisture is determined at each of six pressures. The objective is to develop a response curve for prediction of soil moisture from pressure readings. (Data courtesy of Joanne Rebbeck, North Carolina State University.)

(a) Plot percent moisture against pressure for each soil type. Search for a transformation on X or Y or both that linearizes the relationship for all soils. Fit your transformed data and test homogeneity of the responses over the six soil types.

(b) Use the nonlinear model Y_ij
= α_j
+ β_jX^γ
_i
+ ϵ_ij
to summarize the relationship between Y and X on the original scale, where Y = moisture, X = pressure, and j indexes soil types. (Caution: Your nonlinear program may not be able to iterate γ across γ = 0 and you may have to try both γ > 0 and γ
_j
and β_j
for each soil. Fit the reduced model for H₀: β₁
= β₂
= β₃
= β₄
= β₅
= β₆
and test this composite null hypothesis. Plot the residuals for your adopted model and summarize the results. What does the estimate of γ suggest about the adequacy in Part (a) of only a logarithmic transformation on pressure?