For linear regression calculated for a sample of n = 20 pairs of X and Y values, what is the value for degrees of freedom for the predicted portion of the Y-score variance, MSregression?

The degrees of freedom for the model on this case is given by where k =1 represent the number of variables.

The degrees of freedom for the error on this case is given by . Since we know we can find N.

And the total degrees of freedom would be

Step-by-step explanation:

Previous concepts

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".  

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"  

When we conduct a multiple regression we want to know about the relationship between several independent or predictor variables and a dependent or criterion variable.

Solution to the problem

If we assume that we have independent variables and we have   individuals, we can define the following formulas of variation:  

And we have this property  

The degrees of freedom for the model on this case is given by where k =1 represent the number of variables.

The degrees of freedom for the error on this case is given by . Since we know  we can find N.

And the total degrees of freedom would be