Answer:
Part (A) The Error Degrees of Freedom for this example is 154.
Part (B) The Error Degrees of Freedom for this example is 152.
Step-by-step explanation:
Consider the provided information.
The categorical variable has 4 levels.
It is given that 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.
Thus, the total number of coefficients(p) = 2+(4-1)=5
It is given that Error Degrees of Freedom are calculated as n - p - 1
Substitute n = 160 and p=5 in above formula.
Hence, the Error Degrees of Freedom for this example is 154.
Part B: Categorical variable with 3 levels and another categorical variable with 4 levels. Also a model with 2 numerical explanatory variables both with a linear relationship to the response.
Thus, the total number of coefficients(p) = 2+(3-1)+(4-1)=7
It is given that Error Degrees of Freedom are calculated as n - p - 1
Substitute n = 160 and p=5 in above formula.
Hence, the Error Degrees of Freedom for this example is 152.