# $R^2$ associated with a restricted LS estimator is never larger that that of the unrestricted LS estimator

Prove that the $$R^2$$ associated with a restricted least squares estimator is never larger than that associated with the unrestricted least square estimator.

So, I tried doing this question but I can't find a way to beginning working through it. I would really appreciate if someone could help me work through this and understand it.

• This reads like a homework/assignment question, in which case you should consider adding the self-study tag. – Rickyfox Jan 31 at 12:14
• Hint: The unrestricted estimator is, by its definition, the one that minimizes the sum of squared residuals. Check how $R^2$ can be written as a function of this sum of squared residuals. – Christoph Hanck Jan 31 at 13:52