Chapter 14.2, Problem 29E

The article “The Undrained Strength of Some Thawed Permafrost Soils” (Canadian Geotechnical Journal [1979]: 420–427) contained the accompanying data on y = Shear strength of sandy soil (kPa), x₁ = Depth (m), and x₂ = Water content (%). The predicted values and residuals were calculated using the estimated regression equation

$\begin{array}{l}\hat{y}=-151.36-16.22x_1+13.48x_2\\ +0.094x_3-0.253x_4+0.492x_5\end{array}$

where $x_3=x_1^2$, $x_4=x_2^2$, and x₅ = x₁x₂.

1. a. Use the given information to calculate SSResid, SSTo, and SSRegr.
2. b. Calculate R² for this regression model. How would you interpret this value?
3. c. Use the value of R² from Part (b) and a 0.05 level of significance to carry out a model utility F test.