The root mean square error (RMS Error), or root mean square deviation, is a measure of the differences between predicted values and observed values.

where are the residuals (difference between the observed value and the estimated value) for each data point.

Hint

Similar to variance, RMS error use the mean of the squared residuals. Using just the mean of the residuals in linear regression would always result in zero.

Given data of size 2, where the 2 values have residuals of 9 and 6, what is the population RMS error?

RMS Error in Linear Regression

In linear regression, a quick formula to calculate the RMS Error is

where is the correlation coefficient.

We can see that with perfect correlation (i.e. ), RMS Error is 0. And when , RMS Error is the standard deviation of the dependent variable.