2 Correlation

2 Correlation - Dr Harvey A Singer School of Management...

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© 2007 by Harvey A. Singer 1 OM 210 Statistical Analysis for  Management Simple Linear Regression and Correlation Part 2: Correlation Dr. Harvey A. Singer School of Management George Mason University

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© 2007 by Harvey A. Singer 2 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 3 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

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© 2007 by Harvey A. Singer 4 How Good is the Model? Used regression to calculate the equation of the best fitting straight line through all the data. Now, how good is that model at fitting all the data? How strongly are the variables related to each other? • Probably should have asked this in the first place. Answer: Evaluate the model. By looking at it. By thinking about. By measuring it statistically. • With correlation. With determination.
© 2007 by Harvey A. Singer 5 Evaluation of the Regression Model Visual. Does the model look good? Does it appear from a graph that the data follow and are aligned with the linear trend? Logical. Is the model reasonable? Does the model make sense? Statistical. Quantitative measures of the aptness and appropriateness of the regression model. Answers the question “How good or not is the linear regression model?”

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© 2007 by Harvey A. Singer 6 Logical Evaluation of the Regression Model Does the algebraic sign of the slope b 1 make sense? Does the sign make good business or economic sense? Business or economic logic should indicate whether the relationship is an increasing ( b 1 > 0) or a decreasing ( b 1 < 0) relationship. If the algebraic sign of b 1 does not make sense, then this indicates that something is wrong with the regression model. Modeling error. Underspecified model: use multiple regression.
© 2007 by Harvey A. Singer 7 Statistical Evaluation of the Regression Model Correlation. Correlation coefficient. Explanatory power. Coefficient of determination. Error decomposition. Standard error of the regression. Estimation and significance. Likely ranges of slope (

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2 Correlation - Dr Harvey A Singer School of Management...

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