Question About Degrees of Freedom

Guys, I just started my review for CFA Level2 exam. I have a question about degree of freedom. Under the ANOVA Table section, can anyone explain to me why the Regression(explained)'s Degree of Freedom is 1, Total Degrees of Freedom is n-1? I thought the degree of freedoms for regression is n-2. Thanks for all your help!

N= No of observations

k= number of parameters

In ANOVA tabel the regression df = k (number of parameters) and error df is n-k-1.

Therefore in simple models with only one parameter b1, k is always 1 and n-k-1 = n-2 df.

Keep in mind what the (n-k-1) df are use for-- its for estimating the error variance. Also, simple models have TWO estimated parameters if the intercept is fit (bo and b1). The K df refers to non-intercept parameters estimated.

n-1 is for estimating the variance (total) of the DV.

If it helps to keep this straight, remember two things:

  1. Total Variance of Y (DV) = Error (unexplained) Variance + Explained Variance (regression)

  2. Total DF = Error DF + Regression DF

If we know two of the df values, we can check ourselves on the other.

For example n=100, with a regression estimating k=3 parameters (not including intercept)

We know total Df is n-1

Regression Df is 3

Error (residual) Df must be: Total DF - Regression DF = (n-1) - k = 99-3 = 96 = n-k-1 = 100-3-1

The individual degrees of freedom must add to the total. It’s helpful to realize these relationships now, as it can be helpful at speeding up your calculations (or filling in incomplete tables).

Edited in bold to make my example more explicit…


Thanks for the clear explanation. Your responses about regression models always help me a lot to get more familiar with this matter.


No problem. I’m glad you find it helpful.

I understand now!! Thanks you guys so much for the useful explanation!

Good to hear!