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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.

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  • $\begingroup$ This reads like a homework/assignment question, in which case you should consider adding the self-study tag. $\endgroup$ – Rickyfox Jan 31 at 12:14
  • $\begingroup$ 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. $\endgroup$ – Christoph Hanck Jan 31 at 13:52

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