Apr 22, 2017
Estimating the Standard Deviation
So far, β₀ and β₁ were found to be estimated using b₀ and b₁, respectively. Now the focus is on estimating the third parameter σ.
The standard deviation σ measures the variability of the response variable about the true regression line for any given value of X.
The residuals eᵢ measure the variability of the response variable about the estimated regression line for a given value of X.
Therefore,the estimator for the unknown parameter σ is a function of the residuals.
For a simple linear regression, the estimate of σ is the standard error sₑ with n – 2 degrees of freedom.
Notice that sₑ² is the average of the squared residuals.