Give the formula for the slope of the regression for Y on X 1 , and for Y on X 2 . Give the value of the slope of the regression for X 2 on X 1 . Give formulas for the residuals for the regressions of...

Give the formula for the slope of the regression for Y on X₁, and for Y on X₂. Give the value of the slope of the regression for X₂
on X₁.

Give formulas for the residuals for the regressions of Y on X₁
and for X₂
on X₁. The plot of these two sets of residuals corresponds to the added-variable plot for X₂.

Compute the slope of the regression corresponding to the added variable plot for the regression of Y on X₂
after X₁, and show that this slope is exactly the same as the slope for the simple regression of Y on X₂
ignoring X₁. Also find the intercept for the added variable plot.