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

Oct 27, 2015

$S S R e g \le S S T$

#### Explanation:

Note that ${R}^{2} = \frac{\text{SSReg}}{S S T}$ where SST= SSReg +SSE and we know that sum of squares are always $\ge 0$.

So $S S E \ge 0$
$\implies S S R e g + S S E \ge S S R e g$
$\implies S S T \ge S S R e g$
$\implies \frac{S S R e g}{S S T} \le 1$
$\implies {R}^{2} \le 1$