Construct a figure similar to Figure 6.3 except draw the projection of Y onto the space defined by X 1 . Similarly, draw the projection of Y onto the space defined by X 2 . (a) Approximate the values...

Construct a figure similar to Figure 6.3 except draw the projection of Y onto the space defined by X₁. Similarly, draw the projection of Y onto the space defined by X₂.

(a) Approximate the values of the simple regression coefficients in each case and compare them to the partial regression coefficients in Figure 6.3.

(b) Identify the residuals vector in both cases and in Figure 6.3.

(c) Convince yourself that the shortest residuals vector is the one in Figure 6.3.

 Figure 6.3