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Multiple Regression Lite

# Multiple Regression Lite - Dr Harvey A Singer School of...

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© 2007 by Harvey A. Singer 1 OM 210 Statistical Analysis for  Management Multiple Linear Regression Dr. Harvey A. Singer School of Management George Mason University

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© 2007 by Harvey A. Singer 2 Multiple Regression Learning Objectives: The multiple regression model. Interpretation of coefficients. The multiple coefficients of determination. Prediction. Estimation.
© 2007 by Harvey A. Singer 3 Purposes Here we extend the simple linear regression model, and allow for any number of independent “predictor” variables. We expect to build a model that fits the data better than the simple linear regression model (using just a single predictor variable).

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© 2007 by Harvey A. Singer 4 Topics Multiple linear regression. Basic concepts. Least squares method. Fitting a plane to the data. Model assumptions. Evaluating the regression model. Coefficients of determination. Prediction by multiple regression.
© 2007 by Harvey A. Singer 5 Organization Basic concepts and motivations Fitting a plane by least squares regression Model assumptions Regression modeling Computer calculation of the equation Using the equation Evaluating the model Coefficient of determination Prediction by regression

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© 2007 by Harvey A. Singer 6 Methodology We will use computer printout to: Assess the model How well it fits the data. Is it useful? Are any required conditions violated? Employ the model Interpreting the coefficients. Predictions using the prediction equation. Estimating the expected value of the dependent variable. Demonstrate by examples.
© 2007 by Harvey A. Singer 7 But First … But first an example.

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© 2007 by Harvey A. Singer 8 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 (\$1000’s) for a sample of 20 programmers chosen at random is shown in the table on the next slide. Programmer Salary Survey
© 2007 by Harvey A. Singer 9 Exp (yr) Score Salary (\$K) Exp (yr) Score Salary (\$K) 4 78 24 9 88 38 7 100 43 2 73 26.6 1 86 23.7 10 75 36.2 5 82 34.3 5 81 31.6 8 86 35.8 6 74 29 10 84 38 8 87 34 0 75 22.2 4 79 30.1 1 80 23.1 6 94 33.9 6 83 30 3 70 28.2 6 91 33 3 89 30 Programmer Salary Survey

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© 2007 by Harvey A. Singer 10 Programmer Salary Survey Salary regressed on years of experience x 1 . Y = 1.62 x 1 + 22.811. R 2 = 0.7316 and r = 0.8553. ___ Y = 1.62x + 22.811 R 2 = 0.7316 0.0 10.0 20.0 30.0 40.0 50.0 0 5 10 15 Years of Experience, x1 Salary, y
© 2007 by Harvey A. Singer 11 Programmer Salary Survey Salary regressed on test score x 2 . Y = 0.4344 x 2 - 4.7097. R 2 = 0.3466 and r = 0.5887. ___ Y = 0.4344x - 4.7097 R 2 = 0.3466 0.0 10.0 20.0 30.0 40.0 50.0 50 60 70 80 90 100 Test Score, x2 Salary, y

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© 2007 by Harvey A. Singer 12 Observations Regressing with just years of experience accounts for only 73.16% of the variation in the annual salary data.
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