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I have a dataset, in which I have multiple OUTPUT vars, let's say $Y_1, Y_2, Y_3$. All are numeric. I also have multiple input, $X_1,X_2,X_3,X_4$. The $Y_1, Y_2$ and $Y_3$ depend on all $X_i$ vars.

I have used linear regression in past. If there was just one $Y$, I could have easily used it. I need to predict $Y_1, Y_2$ and $Y_3$ in this case. How to go about it? Is there a package in sklearn/R which can help? Any algorithm?

That would be your approach towards such a problem?

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You can use Multivariate Multiple Linear Regressior like blow:

fit <- lm(cbind(Y1, Y2) ~ X1 + X2 + X3, data=train_set)
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