Error Degrees of Freedom are calculated as n - p - 1 for multiple regression mod

Question

Error Degrees of Freedom are calculated as n - p - 1 for multiple regression models. The p represents the number of coefficients (not including the intercept) in the estimated model. Part A: Report the Error Degrees of Freedom for this example: Assume 160 observations are used to estimate a model with 2 numerical explanatory variables both with a linear relationship to the response and 1 categorical explanatory variable. The categorical variable has 4 levels. Part B: Assume 160 observations are used to estimate a model with 2 numerical explanatory variables both with a linear relationship to the response. In addition there is one categorical variable with 3 levels and another categorical variable with 4 levels. Report the Error Degrees of Freedom

Explanation / Answer

A. n=160,

2 numerical variable & 1 categorical variable with 4 levels.

p=2+4=6

Error degrees freedom = n-p-1

= 160 - 6 - 1

= 153

B.

n=160

2 numerical variable & 1 categorical with 3 level & 1 categorical with 4 levels

p=2+3+4=9

error degrees of freedom = n - p -1

= 160 - 9 - 1

= 150

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