How $R^2$ values in simple linear regression bound $R^2$ in multiple linear regression

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A simple linear regression on x1 and y yields R^2 of 0.2

A simple linear regression on x2 and y yields R^2 of 0.1

What is a upper and lower bound of R^2 if we do a multiple linear regression on x1, x2 and y?

My guess on the lower bound is 0.2 if x1 and x2 are perfectly correlated, but is the upper bound 0.3? Or little bit less than 0.3?

Kodiologist

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asked Mar 18, 2017 at 17:49

tsilaeri

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$\begingroup$ If this is homework, add the [self-study] tag. $\endgroup$
– Kodiologist
Mar 18, 2017 at 18:43
1

$\begingroup$ If the x1 and x2 are orthogonal, they add up to 0.3. That's the upper bound. $\endgroup$
– ABCD
Mar 20, 2017 at 3:32
$\begingroup$ @Kodiologist No, it is not a homework, and I don't know why you're making that assumption. It was on my interview, and the interviewer gave me a strange look when I said maximum was 0.3, so I'm just asking here to confirm what's the right answer. $\endgroup$
– tsilaeri
Mar 20, 2017 at 5:29

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