Lecture10-Class - Lecture 10 Simple Regression Analysis...

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Lecture 10 Simple Regression Simple Regression Analysis Analysis
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Learning Objectives Compute the equation of a simple regression line from a  sample of data, and interpret the slope and intercept of  the equation Understand the usefulness of residual analysis in testing  the assumptions underlying regression analysis and in  examining the fit of the regression line to the data Compute a standard error of the estimate and interpret  its meaning Compute a coefficient of determination and interpret it Test hypotheses about the slope of the regression model  and interpret the results Estimate values of dependent variable y using the  regression model
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Regression and  Correlation Regression analysis  is  the process of  constructing a mathematical model or  function that can be used to predict or  determine one variable by another  variable Correlation  is  a measure of the degree of  relatedness of two variables
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Simple Regression  Analysis Bivariate (two variables) linear regression --  the most elementary regression model dependent variable,  the variable to be predicted usually called  y independent variable,  the predictor or explanatory  variable , usually called  x
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CD Sales and Concert  Attendance
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Scatter Plot of CD Sales and  Concert Attendance
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Determining the Equation  of the Regression Line The equation of a  line is given by: where: slope of the line intercept of the line y mx c m c y = + = =
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Determining the Equation of  the Regression Line Deterministic Regression Model – mathematical  models that produce an ‘exact’ output for a given input y =  β 0  +  β 1 x Probabilistic Regression Model- a model that includes  an error term that allows for various values of output to  occur for a given value of input y =  β 0  +  β 1 x +  ε β 0  and  β 1  are population parameters β 0  and  β 1  are estimated by sample statistics b 0  and b 1
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Equation of the Simple  Regression Line y y b b where x b b y of value predicted the ˆ slope sample the intersept sample the : ˆ 1 0 1 0 = = = + =
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This note was uploaded on 04/14/2010 for the course ECMT 1010 taught by Professor Vadimtimovsky during the Three '10 term at University of Sydney.

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Lecture10-Class - Lecture 10 Simple Regression Analysis...

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