Regression

While correlation measures how strongly two variables are associated, Regression goes a step further and estimates the actual functional relationship between them, allowing us to predict the value of one variable (the dependent variable) from the value of another (the independent variable).

Because either variable can be chosen as the one being 'explained', there are two regression lines:

• Regression of Y on X — used to estimate Y from a given value of X: $Y - \bar{Y} = b_{yx}(X - \bar{X})$, where $b_{yx} = \dfrac{\sum xy}{\sum x^2}$.
• Regression of X on Y — used to estimate X from a given value of Y: $X - \bar{X} = b_{xy}(Y - \bar{Y})$, where $b_{xy} = \dfrac{\sum xy}{\sum y^2}$. …