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**Unformatted text preview: **13- 1Chapter ThirteenLinear Regression and CorrelationLinear Regression and CorrelationGOALSWhen you have completed this chapter, you will be able to:ONEDraw a scatter diagram.TWOUnderstand and interpret the terms dependentvariable and independent variable.THREECalculate and interpret the coefficient of correlation, the coefficient of determination, and the standard error of estimate.FOURCalculate the least squares regression line and interpret the slope and intercept values.Goals13- 2Correlation AnalysisThe Independent Independent VariableVariableprovides the basis for estimation. It is the predictor variable.Correlation AnalysisCorrelation Analysisis a group of statistical techniques to measure the association between two variables.A Scatter DiagramScatter Diagramis a chart that portrays the relationship between two variables.The Dependent Dependent VariableVariableis the variable being predicted or estimated.Advertising Minutes and $ Sales510152025307090110130150170190Advertising MinutesSales ($thousands)13- 3The Coefficient of Correlation, rNegative values indicate an inverse relationship and positive values indicate a direct relationship.The Coefficient of CorrelationCoefficient of Correlation(r) is a measure of the strength of the relationship between two variables.-11Pearson's r Also called Pearson’s rand Pearson’s product moment correlation coefficient.It requires interval or ratio-scaled data.It can range from -1.00 to 1.00.Values of -1.00 or 1.00 indicate perfect and strong correlation.Values close to 0.0 indicate weak correlation.13- 4Perfect Negative Correlation0 1 2 3 4 5 6 7 8 9 1010987654321XY13- 50 1 2 3 4 5 6 7 8 9 1010987654321XYPerfect Positive Correlation13- 60 1 2 3 4 5 6 7 8 9 1010987654321XYZero Correlation13- 70 1 2 3 4 5 6 7 8 9 1010987654321XYStrong Positive Correlation13- 8Formula for rWe calculate the coefficient of correlation from the following formula.r=Σ(X – X)(Y – Y)(n-1)sxsy13- 9Coefficient of DeterminationIt is the square of the coefficient of correlation. It ranges from 0 to 1.It does not give any information on the direction of the relationship between the variables. The coefficient of determinationcoefficient of determination(r2) is the proportion of the total variation in the dependent variable (Y) that is explained or accounted for by the variation in the independent variable (X).13- 10Example 1Dan Ireland, the student body president at Toledo State University, is concerned about the cost to students of textbooks. He believes there is a relationship between the number of pages in the text and the selling price of the book....

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