Chapter 15

# Chapter 15 - 1 Spring 2011 Dr Kameli a Petrova School of...

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Unformatted text preview: 1 Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 1 Business Statistics II ECO 362: Sections A & B Chapter 15 Multiple Regression Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 2 Multiple Regression s Multiple Regression Model s Least Squares Method s Multiple Coefficient of Determination s Model Assumptions s Testing for Significance s Estimation and Prediction s Qualitative Independent Variables s Residual Analysis Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 3 Describes how the dependent variable y is related to the independent variables x 1 , x 2 , . . . x p and an error term is called the multiple regression model. Multiple Regression Model y = β + β 1 x 1 + β 2 x 2 +. . . + β p x p + ε β , β 1 , β 2 , . . . , β p are the parameters, and ε is a random variable called the error term Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 4 A simple random sample is used to compute sample statistics b , b 1 , b 2 , . . . , b p that are used as the point estimators of the parameters β , β 1 , β 2 , . . . , β p . Estimated Multiple Regression Equation ^ y = b + b 1 x 1 + b 2 x 2 + . . . + b p x p The estimated multiple regression equation is: Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 5 Least Squares Method s Least Squares Criterion 2 ˆ min ( ) i i y y- ∑ Computation of Coefficient Values The formulas for the regression coefficients b , b 1 , b 2 , . . . b p involve the use of matrix algebra. We will rely on computer software packages to perform the calculations. Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 6 Multiple Regression Model Example: Programmer Salary Survey: A software firm collected data for a sample of 20 computer programmers. A suggestion was made that regression analysis could be used to determine if salary was related to the years of experience and the score on the firm’s programmer aptitude test. The years of experience, score on the aptitude test, and corresponding annual salary (\$1000s) are given for a sample of 20 programmers. 2 Spring 2011 Dr. Kameli a Petrova School of Business and Economics SUNY Plattsburgh Slide 7 Suppose we believe that salary ( y ) is related to the years of experience (...
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Chapter 15 - 1 Spring 2011 Dr Kameli a Petrova School of...

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