# Regression model F test on different response variables?

I am comparing two different models (multiple linear model).

Basically the explanatory variables remain the same while response variable are different.

$Model\ 1 - Y_1 = X_1+X_2+X_3$

$Model\ 2 - Y_2 = X_1+X_2+X_3$

I have results from R for both models.

I am just wondering if two of these results eg $F$-statistics, $p$-value, $R^2$, RSS are comparable. So can I say model 1 is better because p-value is smaller. etc ?

From what I learned from class, I only compared models which had the same response variable and different explanatory variables.

• Have a look at the following posts, maybe they are helpful: first, second, third. – COOLSerdash Jun 6 '13 at 16:33
• Is there a functional relationship between $Y_1$ and $Y_2$, ie, can we write $Y_1=g(Y_2)$? Or merely a stochastic relationship ($Y_1 = g(Y_2) +$ error)? – Andrew M Oct 9 '14 at 17:30
• If $Y_1$ and $Y_2$ are both measuring the same kind of variable in the same units, so that the coefficients in the two equations are measuring the same thing, the coefficients can be compared (indeed a CI for their difference can be generated, for example). However, in that case it's more common to combine the two into a single equation and add a dummy variable for the data set (which main effect picks up difference in intercept), whose interactions can be used to pick up differences in slope coefficients. – Glen_b Nov 11 '14 at 22:28