1.4. Regression, Covariance and Correlation Q&A

• Thinking back to learning about covariance and correlation, which of the two do you think will be more closely related to the regression slope?

Click to reveal answer

The covariance. Both the covariance and the regression slope tell us something about how much x increases with y and vice versa. They are measured in the units of our measurements, rather than being standardized (like the correlation coefficient).

• How are correlation and regression similar?

Click to reveal answer

Both methods will tell us the strength and direction of the association between two variables.

• What can we do with regression that we can’t do with correlation?

Click to reveal answer

The correlation, unlike the slope \(b\), treats \(x\) and \(y\) symmetrically. We can use regression to calculate predicted values (\(\hat{y}\)), and we can use these predicted values to find residuals for each data point. We can use these residuals to get an idea of how well the regression line fits the observed data points.