Relationship between averages of two variables and the slope of their regression line

Question

Suppose the least-squares regression line for $y$ and $x$ is $y = kx$. Given that $0 < k < 1$, can we say anything about the means of $y$ and $x$? Can we infer that $\bar{y} < \bar{x}$?

Answer 1

As I recall, the least squares coefficient for $y = kx$ is $k = \frac{\sum xy}{\sum x^2} $.

This doesn't say anything about the means of $x$ and $y$, but does imply imformation about the means of $xy$ and $x^2$.