A regression model is to be developed for predicting the

Chapter 12, Problem 6E

(choose chapter or problem)

A regression model is to be developed for predicting the ability of soil to absorb chemical contaminants. Ten observations have been taken on a soil absorption index (y) and two regressors: \(x_1=\) amount of extractable iron ore and \(x_2=\) amount of bauxite. We wish to fit the model \(y=\beta_0+\beta_1x_1+\beta_2x_2+\epsilon\). Some necessary quantities are:

\(\begin{aligned} \left(\mathbf{X}^{\prime} \mathbf{X}\right)^{-1} &=\left[\begin{array}{ccc} 1.17991 & -7.30982 \mathrm{E}-3 & 7.3006 \mathrm{E}-4 \\ -7.30982 \mathrm{E}-3 & 7.9799 \mathrm{E}-5 & -1.23713 \mathrm{E}-4, \\ 7.3006 \mathrm{E}-4 & -1.23713 \mathrm{E}-4 & 4.6576 \mathrm{E}-4 \end{array}\right] \\ \mathbf{X}^{\prime} \mathbf{y} &=\left[\begin{array}{r} 220 \\ 36,768 \\ 9,965 \end{array}\right] \end{aligned}\)

(a) Estimate the regression coefficients in the model specified.

(b) What is the predicted value of the absorption index y when \(x_1=200\) and \(x_2=50\)?