Multiple Regression 9.4 SECTION 9.4 Multiple Regression 509 What You Should Learn How to use technology to find and interpret a multiple regression equation, the standard error of estimate, and the coefficient of determination How to use a multiple regression equation to predict y-values Finding a Multiple Regression Equation Predicting y-Values Finding a Multiple Regression Equation In many instances, a better prediction model can be found for a dependent (response) variable by using more than one independent (explanatory) variable. For instance, 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. Models that contain more than one independent variable are called multiple regression models. A multiple regression equation for independent variables x1, x2, x3, . . ., xk and a dependent variable y has the form ny = b + m1x1 + m2x2 + m3x3 + g+ mkxk where ny is the predicted y@value for given x i values and b is the y@intercept. The y@intercept b is the value of ny when all x i are 0. Each coefficient mi is the amount of change in ny when the independent variable x i is changed by one unit and all other independent variables are held constant. DEFINITION Because the mathematics associated with multiple regression is complicated, this section focuses on how to use technology to find a multiple regression equation and how to interpret the results. Finding a Multiple Regression Equation A researcher wants to determine how employee salaries at a 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 in the table. Employee Salary (in dollars), y Employment (in years), x1 Experience (in years), x2 Education (in years), x3 A 57,310 10 2 16 B 57,380 5 6 16 C 54,135 3 1 12 D 56,985 6 5 14 E 58,715 8 8 16 F 60,620 20 0 12 G 59,200 8 4 18 H 60,320 14 6 17 Use Minitab to find a multiple regression equation that models the data. EXAMPLE 1 Tech Tip Detailed instructions for using Minitab and Excel to find a multiple regression equation are shown in the technology manuals that accompany this text.
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