Question

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

Answer 1

`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`