Assumption that more is better satisfied for both goods

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Q. A linear regression yields β1=0. Elucidate how that R^2=0

A linear regression yields R^2=0. Does this imply that β1=0?

Elucidate how that the regression R^2 in the regression of Y on X is the squared value of the sample correlation between X also Y. That is, Elucidate how that R^2=r^2xy

Elucidate how that the R^2 from the regression of Y on X is the same as the R^2 from the regression of X on Y.

Q. Consider the utility function U(x,y) = 3x + y, with MUx=3 also MUy = 1. Is the assumption that more is better satisfied for both goods?

 

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