Question

does the error term and the residual term mean the same thing for multiple regression model ?

Answer 1

Theoretically, yes. The error term and the residual term represent the same thing for multiple regression model, however there lies some important difference between them which is worth to be known even if they are usually used inter-changeably in the regression models. In general, it's not possible to calculate the error term whereas the residual can be calculated. This is because the error term represents the sum of difference between the observed values and the corresponding population values, whereas the residual represents the sum of difference between the observed values and the corresponding sample values.

Since, we usually use the outcomes of a sample as an estimate for the population parameters, residuals are also used as an estimate for the error term in the similar way.

Hope this answers your query!