If the correlation between $x$ and $y$ is not zero, then the variability about the estimated regression line will be less than the total variability in $y$.

Question

Quizplus · Accepted Answer

When the correlation between $x$ and $y$ is not zero, it indicates that there is a linear relationship between the two variables. This means that some of the variability in $y$ can be explained by $x$ through the regression line, reducing the unexplained variability compared to the total variability in $y$.

If the Correlation Between xxx And yyy Is Not Zero, Then the Variability About the Estimated Regression

If the Correlation Between $x$ And $y$ Is Not Zero, Then the Variability About the Estimated Regression