Linear Equations

In algebra, you learned that you can write an equation of any straight line in the form: y = mx + b. This equation is called Slope Intercept Form. The variable m represents the slope of the line and the variable b represents the y-intercept of the line (where the line crosses the y-axis).

In the line shown below, the equation of that line, in slope intercept form is y = 1/2 x + 1 because the slope of the line is 1/2 and the y-intercept is 1.

The equation of a regression line follows a similar form: \( \hat{y}=mx + b \) where \( \hat{y} \), pronounced y-hat, represents the predicted y-value. The variables m and b also represent the slope and y-intercept, respectively.

The difference between the methods you learned in algebra to find the equation of a line and the method for finding the equation of a regression line is that a regression line takes into consideration ALL the data points, x and y, in our data set to determine the equation \( \hat{y}=mx + b \).