The data in the next were obtained in a forestry study of certain characteristics of a stand of pine trees including A, age of a particular pine stand; HD, the average height of dominant trees in feet; N, the number of pine trees per acre at age A; and MDBH, the average diameter measured at breast height (4.5 feet above ground). A theoretical analysis suggested that the following model is appropriate: Model (Y = MDBH|X1 = HD, X2 = A × N, X3 = HD/N). (a) Fit this model to the data. Compute R2 and R2 a (the adjusted R-squar. (b) Test the hypothesis H0 : β3 = 0 against H1 : β3 = 0. State your conclusions. (c) Fit the reduced Model (Y = MDBH|X1 = HD, X2 = A × N). Compute R2 and R2 a for the reduced model. (d) For each model prepare a of fitted values, standard error of prediction, etc., similar in format to that. Compare the full and reduced models by comparing the standard errors of prediction. Which model performs better?
(Source: R.H. Myers (1990), Classical and Modern Regression with Applications, 2nd ed., PWS-Kent, Boston. Used with permission.)