Errors and residuals

The error, ε, for any data point is its vertical distance from the regression line.

In practice, the slope and intercept of the regression line are unknown, so the errors are also unknown values, but the least squares residuals provide estimates.

Estimating the error standard deviation

The third unknown parameter of the normal linear model, σ, is the standard deviation of the errors,

σ  = st devn( ε )

σ can be estimated from the least squares residuals, {ei},

This is similar to the formula for the standard deviation of the residuals, but uses the divisor (n − 2) instead of (n − 1). It describes the size of a 'typical' residual.

Example