Question

​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?

Answer 1

Answer:

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

The degrees of freedom for the error on this case is given by $df_{error}=N-k-1=20-1-1=18$. Since we know we can find N.

And the total degrees of freedom would be $df=N-1=20 -1 =19$

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 $k=1$ independent variables and we have  $j=1,\dots,j$ individuals, we can define the following formulas of variation:  

$SS_{total}=\sum_{j=1}^n (y_j-\bar y)^2$  

$SS_{regression}=SS_{model}=\sum_{j=1}^n (\hat y_{j}-\bar y)^2$  

$SS_{error}=\sum_{j=1}^n (y_{j}-\hat y_j)^2$  

And we have this property  

$SST=SS_{regression}+SS_{error}$  

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

The degrees of freedom for the error on this case is given by $df_{error}=N-k-1=20-1-1=18$. Since we know  we can find N.

And the total degrees of freedom would be $df=N-1=20 -1 =19$