Question

A company that manufactures computer chips wants to use a multiple regression model to study the effect that two variables have on , total daily production cost (in s of dollars). Those two variables are the following. daily production volume (in s of units) daily amount of time involved in production (in hours) If a regression model is estimated using observations on each of these variables, what are the degrees of freedom (df) for the regression sum of squares, error sum of squares, and total sum of squares? (a) df for the regression sum of squares: (b) df for the error sum of squares: (c) df for the total sum of squares:

Answer 1

(a) The degrees of freedom (df) for the regression sum of squares is equal to the number of independent variables in the regression model. In this case, there are two independent variables: daily production volume and daily amount of time involved in production. Therefore, the df for the regression sum of squares is 2.

(b) The degrees of freedom (df) for the error sum of squares is equal to the total number of observations minus the number of independent variables in the regression model. Let's assume there are n observations. Since there are two independent variables in the model, the df for the error sum of squares is (n - 2).

(c) The degrees of freedom (df) for the total sum of squares is equal to the total number of observations minus 1. Therefore, the df for the total sum of squares is (n - 1).