Why must the R-Squared value of a regression be less than 1?

1 Answer
Oct 27, 2015

SSReg le SST

Explanation:

Note that R^2= ("SSReg")/(SST) where SST= SSReg +SSE and we know that sum of squares are always ge 0.

So SSE ge 0
implies SSReg +SSE ge SSReg
implies SST ge SSReg
implies (SSReg)/(SST) le 1
implies R^2 le 1