*x-*value and predict a new

*y-*value. In the example you’ve been working through, you take a SAT score and predict a GPA for a Sahutsket University student.

What if you knew more than just the SAT score for each student? What if you had the student’s high-school average (on a 100 scale), and you could use that information, too? If you could combine SAT score with HS average, you might have a more accurate predictor than SAT score alone.

When you work with more than one independent variable, you’re in the realm of *multiple* *regression.* As in linear regression, you find regression coefficients for the best-fitting line through a scatterplot. Once again, *best-fitting* means that the sum of the squared distances from the data points to the line is a minimum.

With two independent variables, however, you can’t show a scatterplot in two dimensions. You need three dimensions, and that becomes difficult to draw.

For the SAT-GPA example, the regression equation translates to

Predicted GPA =a+b_{1}(SAT)+b_{2}(High School Average)

You can test hypotheses about the overall fit, and about all three of the regression coefficients.

Let’s check out the Excel capabilities for finding coefficients.

A few things to bear in mind:

- You can have any number of
*x-*variables. - Expect the coefficient for SAT to change from linear regression to multiple regression. Expect the intercept to change, too.
- Expect the standard error of estimate to decrease from linear regression to multiple regression. Because multiple regression uses more information than linear regression, it reduces the error.