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Unformatted text preview: Ch. 14 Simple Linear Regression If data can be obtained, a statistical procedure called regression analysis can be used to develop an equation showing how the variables are related The variable being predicted is called the dependent variable o The variable or variables being used to predict the value of the dependent variable are called the independent variables o In statistical notation, y denotes the dependent variable and x denotes the independent variable Simple linear regression is the simplest type of regression analysis involving one independent variable and one dependent variable in which the relationship between the variables is approximated by a straight line o Regression analysis involving 2+ independent variables is called multiple regression analysis 14.1 Simple Linear Regression Model Managers of Armands Pizza Parlors believe that quarterly sales for restaurants located by college campuses (denoted y ) are related positively to the size of the student population (denoted by x ) A. Regression Model and Regression Equation The population in this example consists of all the Armands restaurants For every restaurant in the population, there is a value of x (student population) and a corresponding value of y (quarterly sales) The equation that describes how y is related to x and an error term is called the regression model SIMPLE LINEAR REGRESSION MODEL 14.1 y = + 1 x + and 1 are referred to as the parameters of the model, and is a random variable referred to as the error term The error term accounts for the variability in y that cannot be explained by the linear relationship between x and y The population of all Armands restaurants can also be viewed as a collection of subpopulations, one for each distinct value of x Each subpopulation has a corresponding distribution of y values Each distribution of y values has its own mean or expected value The equation that describes how the expected value of y , denoted E(y), is related to x is called the regression equation SIMPLE LINEAR REGRESSION EQUATION 14.2 E(y) = + 1 x The graph of the simple linear regression equation is a straight line; is the y intercept of the regression line, 1 is the slope, and E(y) is the mean or expected value of y for a given value of x B. Estimated Regression Equation If the values of the population parameters and 1 were known, we could use equation 14.2 to compute the mean value of y for a given value of x In practice, the parameter values arent known, and must be estimated using sample data Sample statistics (denoted b and b 1 ) are computed as estimates of the population parameters and 1 Substituting the values of the sample statistics b and b 1 for and 1 in the regression equation, we obtained the estimated regression equation ESTIMATED SIMPLE LINEAR REGRESSION EQUATION 14.3 y = b + b 1 x The graph of the estimated simple linear regression equation is called the...
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 Spring '08
 HERBERT

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