1. Section 9.4 Multiple Regression

2. Section 9.4 Objectives Use a multiple regression equation to predict y-values

3. Multiple Regression Equation In many instances, a better prediction can be found for a dependent (response) variable by using more than one independent (explanatory) variable. For example, a more accurate prediction for the carbon dioxide emissions discussed in previous sections might be made by considering the number of cars as well as the gross domestic product.

4. Multiple Regression Equation * Because the mathematics associated with this concept is complicated, technology is generally used to calculate the multiple regression equation.

5. Predicting y - Values After finding the equation of the multiple regression line, you can use the equation to predict y-values over the range of the data. To predict y-values, substitute the given value for each independent variable into the equation, then calculate ŷ.

6. Example: Finding a Multiple Regression Equation A researcher wants to determine how employee salaries at a certain company are related to the length of employment, previous experience, and education. The researcher selects eight employees from the company and obtains the data shown on the next slide.

7. Example: Finding a Multiple Regression Equation EmployeeSalary, y Employment (yrs), x 1 Experience (yrs), x 2 Education (yrs), x 3 A57,31010216 B57,3805616 C54,1353112 D56,9856514 E58,7158816 F60,62020012 G59,2008418 H60,32014617

8. Example: Predicting y-Values Use the regression equation ŷ = 49,764 + 364x 1 + 228x 2 + 267x 3 to predict an employee’s salary given 12 years of current employment, 5 years of experience, and 16 years of education. Solution: ŷ = 49,764 + 364(12) + 228(5) + 267(16) = 59,544 The employee’s predicted salary is $59,544.

9. Section 9.4 Summary Used a multiple regression equation to predict y- values