The residual sum of the squares is the numerator portion of the formula for the variance of y about the regression line.


True
False

False.

The residual sum of squares (RSS) is the sum of the squared differences between the actual values of the dependent variable (y) and the predicted values from the regression line. It is not directly related to the numerator portion of the formula for the variance of y about the regression line.

The variance of y about the regression line, also known as the explained sum of squares (ESS), measures the amount of variation in the dependent variable (y) that is accounted for by the linear regression model. It represents the sum of the squared differences between the predicted values from the regression line and the mean of the dependent variable. The residual sum of squares is the complement of the explained sum of squares within the total sum of squares (TSS).

To calculate the variance of y about the regression line, you need to divide the explained sum of squares (ESS) by the degrees of freedom associated with the regression model. The formula is as follows:

Variance of y about the regression line = ESS / (n - 2)

Where:
- ESS is the explained sum of squares
- n is the number of observations in the data set
- 2 is the degrees of freedom associated with the regression model (one for the intercept and one for the slope)

So, in summary, the residual sum of squares is not directly related to the numerator portion of the formula for the variance of y about the regression line.