Multiple Regression Lite

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

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© 2010 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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© 2010 by Harvey A. Singer 2 Multiple Regression Learning Objectives: The multiple regression model. Interpretation of coefficients. The multiple coefficients of determination. Prediction. Estimation.
© 2010 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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© 2010 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.
© 2010 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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© 2010 by Harvey A. Singer 6 Methodology We will use a computer output report 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.
© 2010 by Harvey A. Singer 7 But First … But first an example.

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© 2010 by Harvey A. Singer 8 A software firm collected data for a sample of n = 20 computer programmers. Use regression analysis to predict annual salary (in \$K) from an employee’s years of experience and the employee’s score on the firm’s programmer certification test. The years of experience, score on the certification 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
© 2010 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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© 2010 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
© 2010 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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© 2010 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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