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Regression Coefficients

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Parts

Part 1

Suppose that we have two datasets $X$ and $Y$ with $Var(X) = 10$ and $Var(Y) = 20$. We perform the linear regression:

$y \sim \alpha_x + \beta_xx$

and obtain $\beta_x = 1$. Suppose now perform the regression:

$x \sim \alpha_y + \beta_yy$

What is the value of $\beta_y$?