The Regression Line (a Big and Nifty Idea):

Now that we know we have a linear relationship and that SAT and GPA are significantly related, we can just obtain someone's SAT and predict his/her GPA.

To do this, we use the regression line where Y' is the Y score predicted from the X score. To estimate the line, we need to calculate the slope and intercept.

This is the best-fit line and it’s the one through the ellipse. It means that when you have a scattergram, you are going to calculate the equation of the line that zaps right through the middle of the data points. You need the slope and the intercept.

It has been determined that the slope = r(SDy)/SDx) and the Intercept = {r(SDy)/SDx) + Mean of Y}.

Most calculators and computer programs will do this for you.