ESS210B
Prof. Jin-Yi Yu
An Example
qFor a 2-predictor case: r1y = r2y = r12 = 0.50
If only include one predictor (x1) (r2y = r12 =0) è R2=0.25
By adding x2 in the regression (r2y = r12 =0.50) è R2=0.33
In this case, the 2nd predictor improve the regression.
qFor a 2-predictor case: r1y = r12 = 0.50 but r2y = 0.25
If with only x1 è R2=025
Adding x2 è R2=025 (still the same!!)
In this case, the 2nd predictor is not useful.
It is because
r2y £ r1y * r12 = 0.50*0.50 = 0.25