Suppose the $R^2$ value of $x_1$ with $y$ is equal to $0.15$. The $R^2$ value of $x_2$ with $y$ is equal to $0.35$. Can there exist constants $a,b$ such that the variable $X=ax_1+bx_2$ has an $R^2>0.5$ with $y$?
I'm thinking no, but I can't find anything on the subject online to verify this.
I know in some cases this obviously wouldn't be possible (such as if the sum of the r-squared values of the input variables exceed 1). But can it ever be true? Is there a rule related to this subject?
