Chapter 14 Simple Linear Regression

Chapter 14 Simple Linear Regression - Chapter 14 Simple...

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Chapter 14 – Simple Linear Regression - Regression analysis can be used to develop an equation showing how two variables are related - The variable being predicted is the dependent variable , and the variable being used to predict that value of the dependent variable is the independent variable (y denotes the dependent variable and x denotes the independent variable) - The simplest type of regression analysis, simple linear regression , involves one independent variable and one dependent variable where the relationship between the two is approximated by a straight line (regression analysis involving two or more independent variables is multiple regression analysis) Simple Linear Regression Model Regression Model and Regression Equation - The equation that describes how y is related to x and an error term is called the regression model ( Equation 14.1 p. 555 ): y = β 0 + β 1 x + ε - β 0 and β 1 are the parameters of the model, and ε is a random variable referred to as the error term, which accounts for the variability in y that cannot be explained by the linear relationship between x and y - The equation that describes how the expected value of y, denoted E(y), is related to x is the regression equation ( Equation 14.2 p. 556 ): E(y) = β 0 + β 1 x - The graph of this equation is a straight line, with β 0 the y-intercept of the regression line, β 1 the slope, and E(y) the mean or expected value of y for a given value of x Estimated Regression Equation - If the population parameters were known, Equation 14.2 can be used to compute the mean value of y for a given value of x; however the parameter values are not known, and sample statistics are used to estimate the population parameters - Substituting the values of the sample statistics b0 and b1 for β 0 and β 1 in the regression equation, the estimated regression equation ( Equation 14.3 p. 557 ) is obtained: ŷ = b o + b 1 x - The graph of this equation is the estimated regression line, where b 0 is the y-intercept and b 1 is the slope (using the least squares method, these values can be computed in the estimated regression equation) - In general, ŷ is the point estimator of E(y), the mean value of y for a given value of x (known simply as the estimated value of y , since it provides both a point estimate of
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This note was uploaded on 04/07/2008 for the course ANTH 145 taught by Professor Gatewood during the Fall '07 term at Lehigh University .

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Chapter 14 Simple Linear Regression - Chapter 14 Simple...

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