Question

1735 newborns in 2012 were randomly chosen, and their birth weights were determined. A linear regression model was built to investigate the association between birth weight (the outcome) and gestational age (the exposure variable), controlling for sex of the child (1 for female; 0 for male), plurality (1 for twins, triplets, etc; 0 for single births), maternal race (1 for white; 0 otherwise). In the ANOVA table, we see degrees of freedom (DF) for the model and the error. We also see total DF. What is the degrees of freedom associated with the model?

Group of answer choices

a. 4

b. 5

c. 35000

d. 34999

Answer 1

What is the degrees of freedom associated with the model

Answer : 4

Outcome : Birth weight

Predictor variables :

1. gestational age (the exposure variable),

2. controlling for sex of the child (1 for female; 0 for male),

3. plurality (1 for twins, triplets, etc; 0 for single births),

4. maternal race (1 for white; 0 otherwise).

Number of predictor variables = 4

The degrees of freedom for model is one less than the number of parameters being estimated.

There are 4 predictor variables and so there are 4 parameters for the coefficients on those variables. There is always one additional parameter for the constant so there are 4+1 parameters.

But the degrees of freedom is one less than the number of parameters, so there are 4+1 - 1 = 4 degrees of freedom.

That is, the DF  for model (Regression) = # of predictor variables = 4