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Unformatted text preview: DS 101 05/05/2010 16:02:00 1 REGRESSION ANALYSIS In our discussion of regression analysis, we will first focus our discussion on simple linear regression and then expand to multiple linear regression. The reason for this ordering is not because simple linear regression is so simple , but because we can illustrate our discussion about simple linear regression in two dimensions and once the reader has a good understanding of simple linear regression, the extension to multiple regression will be facilitated. It is important for the reader to understand that simple linear regression is a special case of multiple linear regression. Regression models are frequently used for making statistical predictions  this will be addressed at the end of this chapter. Simple Linear Regression Simple linear regression analysis is used when one wants to explain and/or forecast the variation in a variable as a function of another variable. To simplify, suppose you have a variable that exhibits variable behavior, i.e. it fluctuates. If there is another variable that helps explain (or drive) the variation, then regression analysis could be utilized. The variable one wants to explain (or predict or forecast) is called the dependent variable , usually denoted y . The variable one uses to explain/forecast is called the independent variable , usually denoted x . The simple linear regression model is 0 1 y x = + + . Thus, y is a linear function of x plus an error term . y and x are the data. and 1 ( , or beta, is the Greek letter) are the parameters that need to be estimated from the data. (the Greek letter epsilon) is a random variable that we call the error term, which 2 accounts for the variation in the dependent variable y that cannot be explained by the model, the linear relationship between x and y . This error term is assumed to be common variation with the properties of stationary (constant mean and constant variance), independent (random), and normal. To be more specific, the assumptions of the error term are listed below: 1. Stationary : constant mean and constant variance. Constant mean: the average value of the error term is 0. Constant variance: the variance of the error term is the same for all values of the independent variable. To check this assumption, apply the identification tool: Time series plot (...
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This note was uploaded on 05/05/2010 for the course DS 36504 taught by Professor Minli during the Spring '10 term at CSU Sacramento.
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