The diameter of a tree at its breast height is influenced by many factors. The data in Table 9.5 relate the diameter of a particular type of eucalyptus tree to its age, average rainfall at its site, site's elevation, and the wood's mean specific gravity. (The data come from R. G. Skolmen, 1975, "Shrinkage and Specific Gravity Variation in Robusta Eucalyptus Wood Grown in Hawaii." USDA Forest Service PSW-298.)
Assuming a linear regression model of the form
Y = β0 + β1x1 + β2x2 + β3x3 + β4x4 + e
where x1 is the age, x2 is the elevation, x3 is the rainfall, x4 is the specific gravity, and Y is the tree's diameter, test the hypothesis that β2 = 0. That is, test the hypothesis that, given the other three factors, the elevation of the tree does not affect its diameter.