Figure 5

The projection of bp on V _w and V _⊥cw is vector bp _p and bp _⊥cw respectively. Since cw = bw + wg, the projections of bw and wg on V _⊥cw (bw _⊥cw and wg _⊥cw respectively) will be in opposite directions (though parallel). Therefore, if the angle between bw _⊥cw and bp _⊥cw is φ, the angle between wg _⊥cw and bp _⊥cw will be (π - φ). From elementary trigonometry: cos(φ) = -cos(π - φ). Hence, in Model 3, after adjustment for current weight (CW), the P-value for weight gain (WG) is identical to that for birth weight (BW) in Model 1. From the two lines, L _cw1 and L _cw2 running parallel to cw, it is apparent that the absolute values of the two partial regression coefficients for birth weight (BW) and weight gain (WG) are identical.