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1 Regression

# 1 Regression - Dr Harvey A Singer School of Management...

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© 2009 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

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© 2009 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.
© 2009 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.

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© 2009 by Harvey A. Singer 4 Data Presentation The data is presented as ordered data pairs ( x , y ). Also referred to as a “data point.” x is the “independent” variable, which is free to take any value in the specified range. y is the value of the “dependent” variable that depends on, responds to, or is otherwise associated with the value x . Take a sample of size n consisting of n data points. There are n values of x and n values of y written as n ordered pairs.
© 2009 by Harvey A. Singer 5 The Variables An independent variable is used to predict values of the response of some other quantity of interest. Generally denoted by x or as appropriate. If forecasting over time, then use t for time. Also referred to as a predictor or explanatory variable. In a graph, x is always plotted as the abscissa on the horizontal axis. A dependent variable is the quantity of interest that depends on and responds to values of the predictor variables. The value y results from the value assigned to x . Generally denoted by y or as appropriate. E.g., demand, D . Also referred to as a response variable. In a graph, y is always plotted as the ordinate on the vertical axis.

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© 2009 by Harvey A. Singer 6 Concept Are these variables related? Does one variable predict the response of the other variable? Does the value of one of the variables determine the value of the other? If yes, then how? State mathematically the relationship between the variables. As a mathematical function. Calculate the relationship from the sampled data. Measure how good or not is that relationship. How good or not is the regression as a predictive tool.
© 2009 by Harvey A. Singer 7 Objective Can an equation be found from just the data, without having to construct and read a graph? Answer: YES! Use statistics to automate the process of finding the equation of the straight that best fits all of the data.

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1 Regression - Dr Harvey A Singer School of Management...

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