How to interpret the RMSE value generated by a regression model?

Question

What exactly does an RMSE(root mean squared error) value imply? How to interpret it with regards to any regression problem?

Answer 1

As explained in the top answer here, the MSE is the variance of the residuals about the fitted line.

Now since the standard deviation is the square root of the variance, that would make the RMSE the standard deviation of the residuals. It is an estimate $\sigma$ in the linear regression model $Y\mid \mathbf{x} \sim N(\mathbf{x}^T \beta, \sigma^2)$.