Construct a diagram similar to Figure 6.3 except make X 1 and X 2 orthogonal to each other. Convince yourself that, when the independent variables are orthogonal, the simple regression coefficients...

Construct a diagram similar to Figure 6.3 except make X₁
and X₂
orthogonal to each other. Convince yourself that, when the independent variables are orthogonal, the simple regression coefficients from the projection of Y onto X₁
and X₂
separately equal the partial regression coefficients from the projection of Y onto the space defined by X₁
and X₂
jointly.