Q. 14
Question
For each of the sums of squares in regression, state its name and what it measures,
a. SST
b. SSR
c. SSE
Step-by-Step Solution
Verifieda) SST measures how much variation is there in the observed data.
b) SSR measures the variation in the modeling errors.
c) SSE (Sum of squares Error) is the difference between the observed value and the predicted value.
To determine the name of SST and to explain what it measures.
The regression sum of squares is obtained by dividing the corresponding sum of squares by the degrees of freedom. In regression, whether the terms in the model are significant or not is determined by using the mean squares. The mean square is the term obtained by dividing the sum of squares by the degrees of freedom.
SST (Sum of Squares Total) is the squared difference between the observed dependent variable and its mean.
To determine the name of SSR and to explain what it measures.
S S R (Sum of Squares due to Regression) is the sum of the differences between the predicted value and the mean of the dependent variable.
To determine the name of S S E and to explain what it measures.
SSE measures how much variation is there in the modeled values and this is compared to the total sum of squares and to the residual sum of squares.