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Unformatted text preview: Chap 151 Statistics Chapter 15 Multiple Regression Analysis and Model Building Chap 152 Chapter Goals After completing this chapter, you should be able to: explain model building using multiple regression analysis apply multiple regression analysis to business decisionmaking situations analyze and interpret the computer output for a multiple regression model test the significance of the independent variables in a multiple regression model Chap 153 Chapter Goals After completing this chapter, you should be able to: recognize potential problems in multiple regression analysis and take steps to correct the problems incorporate qualitative variables into the regression model by using dummy variables use variable transformations to model nonlinear relationships (continued) Chap 154 The Multiple Regression Model Idea: Examine the linear relationship between 1 dependent (y) & 2 or more independent variables (x i ) ε x β x β x β β y k k 2 2 1 1 + + + + + = k k 2 2 1 1 x b x b x b b y ˆ + + + + = Population model: Yintercept Population slopes Random Error Estimated (or predicted) value of y Estimated slope coefficients Estimated multiple regression model: Estimated intercept Chap 155 Multiple Regression Model Two variable model y x 1 x 2 2 2 1 1 x b x b b y ˆ + + = S l o p e f o r v a r i a b l e x 1 S lo p e fo r v a ria b le x 2 Chap 156 Multiple Regression Model Two variable model y x 1 x 2 2 2 1 1 x b x b b y ˆ + + = y i y i < e = (y – y) < x 2i x 1i The best fit equation, y , is found by minimizing the sum of squared errors, Σ e 2 < Sample observation Chap 157 Multiple Regression Assumptions The model errors are independent and random The errors are normally distributed The mean of the errors is zero Errors have a constant variance e = (y – y) < Errors (residuals) from the regression model: Chap 158 Model Specification Decide what you want to do and select the dependent variable Determine the potential independent variables for your model Gather sample data (observations) for all variables Chap 159 The Correlation Matrix Correlation between the dependent variable and selected independent variables can be found using Excel: Formula Tab: Data Analysis / Correlation Can check for statistical significance of correlation with a t test Chap 1510 Example A distributor of frozen desert pies wants to evaluate factors thought to influence demand Dependent variable: Pie sales (units per week) Independent variables: Price (in $) Advertising ($100’s) Data are collected for 15 weeks Chap 1511 Pie Sales Model Sales = b + b 1 (Price) + b 2 (Advertising) Week Pie Sales Price ($) Advertising ($100s) 1 350 5.50 3.3 2 460 7.50 3.3 3 350 8.00 3.0 4 430 8.00 4.5 5 350 6.80 3.0 6 380 7.50 4.0 7 430 4.50 3.0 8 470 6.40 3.7 9 450 7.00 3.5 10 490 5.00 4.0 11 340 7.20 3.5 12 300 7.90 3.2 13 440 5.90 4.0 14 450 5.00 3.5 15 300 7.00 2.7 Pie Sales Price Advertising...
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 Spring '11
 BobSanders
 Regression Analysis, Model building

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