# Correlation between prediction error and regression dependent variable

I've trained a regression model which predicts the dependent variable from several independent variables. I noticed that there is a strong negative correlation (-0.86) between the dependent variable and the error (prediction - dependent variable). What does this imply?

While it can be caused by all predictions being similar, therefore, creating a linear relationship between the error and the dependent variable, there is also a positive correlation (0.47) between the predictions and the dependent variables.

Is there a way to reduce the errors for larger dependent variable values?

• It is a necessity that $\hat{Y} - Y$ be correlated with $Y$. What you don't want is a correlation between $\hat{Y} - Y$ and $X$ or $\hat{Y}$ as this indicates systematic lack of fit. Jan 16 at 13:48