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 =...

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
= β₀+ β₁
x
₁+ β₂
x
₂+ ?. Some necessary quantities are:

The total sum of squares for
y
is
SS

_T
= 742.00.

(a) Test for significance of regression using α = 0.01. What is the
P-value for this test?

(b) Test the hypothesis
H
₀: β₁= 0 versus
H
₁: β₁≠0 using α = 0.01. What is the
P-value for this test?

What conclusion can you draw about the usefulness of
x
₁as a regressor in this model?