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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 don’t 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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 Regression Analysis, Harvey A. Singer, Dr. Harvey A. Singer

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