The following analysis of variance summarizes the regression of Y on two independent variables plus an intercept. (a) Your estimate of β 1 is 1 = XXXXXXXXXXA friend of yours regressed Y on X 1 and...

The following analysis of variance summarizes the regression of Y on two independent variables plus an intercept.

(a) Your estimate of β₁
is

₁
= 2.996. A friend of yours regressed Y on X₁
and found

₁
= 3.24. Explain the difference in these two estimates.

(b) Label each sequential and partial sum of squares using the Rnotation. Explain what R(β₁|β₀) measures.

(c) Compute R(β₂|β₀) and explain what it measures.

(d) What is the regression sum of squares due to X₁
after adjustment for X₂?

(e) Make a test of significance (use α = .05) to determine if X₁
should be retained in the model with X₂.

(f) The original data contained several sets of observations having the same values of X₁
and X₂. The pooled variance from these replicate observations was s₂
= 3.8 with eight degrees of freedom. With this information, rewrite the analysis of variance to show the partitions of the “residual” sum of squares into “pure error” and “lack of fit.” Make a test of significance to determine whether the model using X₁
and X₂
is adequate.