Section 9.4 Multiple Regression. Section 9.4 Objectives Use a multiple regression equation to...
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Section 9.4 Multiple Regression
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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.
Transcript of Section 9.4 Multiple Regression. Section 9.4 Objectives Use a multiple regression equation to...
Section 9.4
Multiple Regression
Section 9.4 Objectives
• Use a multiple regression equation to predict y-values
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.
Multiple Regression Equation
Multiple regression equation
• ŷ = b + m1x1 + m2x2 + m3x3 + … + mkxk• x1, x2, x3,…, xk are independent variables • b is the y-intercept• y is the dependent variable
* Because the mathematics associated with this concept is complicated, technology is generally used to calculate the multiple regression equation.
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.
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.
Example: Finding a Multiple Regression Equation
Employee Salary, yEmployment
(yrs), x1
Experience (yrs), x2
Education (yrs), x3
A 57,310 10 2 16B 57,380 5 6 16C 54,135 3 1 12D 56,985 6 5 14E 58,715 8 8 16F 60,620 20 0 12G 59,200 8 4 18H 60,320 14 6 17
Example: Predicting y-Values
Use the regression equation ŷ = 49,764 + 364x1 + 228x2 + 267x3
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) = 59,544The employee’s predicted salary is $59,544.
Section 9.4 Summary
• Used a multiple regression equation to predict y-values
