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# isdsexam1 - Ch 14 Simple Linear Regression • If data can...

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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 Manager’s of Armand’s 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 Armand’s 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 = β + β 1 x + ε • β and β 1 are referred to as the parameters of the model, and ε 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 Armand’s 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) = β + β 1 x • The graph of the simple linear regression equation is a straight line; β is the y- intercept of the regression line, β 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 β and β 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 aren’t known, and must be estimated using sample data • Sample statistics (denoted b and b 1 ) are computed as estimates of the population parameters β and β 1 • Substituting the values of the sample statistics b and b 1 for β and β 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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## This note was uploaded on 09/13/2011 for the course ISDS 2001 taught by Professor Herbert during the Spring '08 term at LSU.

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isdsexam1 - Ch 14 Simple Linear Regression • If data can...

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