Chapter 14.2, Problem 21E

The ability of ecologists to identify regions of greatest species richness could have an impact on the preservation of genetic diversity, a major objective of the World Conservation Strategy. The article “Prediction of Rarities from Habitat Variables: Coastal Plain Plants on Nova Scotian Lakeshores” (Ecology [1992]: 1852–1859) used a sample n = 37 lakes to obtain the estimated regression equation

$\begin{array}{l}\hat{y}=3.89+0.033x_1+0.024x_2+0.023x_3\hfill \\ +0.008x_4-0.13x_5-0.72x_6\hfill \end{array}$

where y = Species richness, x₁ = Watershed area, x₂ = Shore width, x₃ = Drainage (%), x₄ = Water color (total color units), x₅ = Sand (%), and x₆ = Alkalinity. The coefficient of multiple determination was reported as R² = 0.83. Use a test with significance level 0.01 to decide whether the chosen model is useful.