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Unformatted text preview: 2007 by Harvey A. Singer 1 OM 210 Statistical Analysis for Management Simple Linear Regression and Correlation Part 1: Regression Dr. Harvey A. Singer School of Management George Mason University 2007 by Harvey A. Singer 2 Before Up until now, have only treated one variable of interest. With descriptive statistics. With probability. With sampling. With estimation. All for just one particular variable of interest. 2007 by Harvey A. Singer 3 What Now? Now, consider two different variables at the same time. They may depend upon each other and may be related to each other. If so, find the relationship between them. So that one variable may be used to predict the other. These are the subjects of regression and correlation. These are the topics of this presentation and the next. 2007 by Harvey A. Singer 4 Topics Simple linear regression. Basic concepts. Least squares method. Model assumptions. Fitting a line to the data. Prediction by regression. Types of regression. Associative regression. Time series regression. Evaluating the regression model. Correlation. Correlation coefficient. Coefficient of determination. Sum of squares decomposition. 2007 by Harvey A. Singer 5 Organization Regression Correlation Basic concepts Fitting a straight line Least squares regression Model assumptions Regression modeling Calculating the equation Using the equation Evaluating the model Calculate correlations Coefficient of determination Calculate determinations Correlation coefficient Relationships 2007 by Harvey A. Singer 6 Why Do You Want the Equation? Answer: PREDICTION! How much will it cost for the year to maintain a machine that is 6 years old? x = 6 is not in the original sample. Have to budget the operating costs now, so dont want to wait to find out. From the equation, set x = 6 and calculate Y = (11 6) + 100 = 166 Predict that a machine 6 years old can be expected to cost $166 to maintain for the year. 2007 by Harvey A. Singer 7 Pros and Cons of the Graphical Method Pros. Direct and straightforward. Logically. Computationally. Cons. Subjective. Graphical technique. Depends on eyeball fit of the line. Which is really only your best guess. Depends on eyeball valuation of points on the line. Reading values from the axes. 2007 by Harvey A. Singer 8 Scattered Data If the example data had been more widely scattered, then the line would not have been so obvious to fit by eye. Age, x (years) Maintenance cost, y ($/year) 4 170 2 115 3 195 5 260 2 164 3 225 4 220 5 195 4 180 3 200 50 100 150 200 250 300 1 2 3 4 5 6 2007 by Harvey A. Singer 9 Need Avoid the subjectivity....
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 Fall '08
 SINGER

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