Simple Linear RegressionSimple Linear Regression ModelingThings to Considered for SLRLeast Square Solution of the Fitted LineMore Regression Summary StatisticsStatistical Inference in SLRSLR: Housing Data ExampleData and Summary StatisticsSLRSimple Linear Regression SLR: Housing Data ExampleChapter 11. Linear RegressionSimple Linear RegressionJC Wang (WMU) Stat2160 S2160, Chapter 11 1 / 53Simple Linear Regression SLR: Housing Data ExampleGoal and Objectivesof Chapter 11Goal: To learn about regression modelingObjectivesTo learn hypotheses testing methodology for the slopeTo understand simple linear regressionTo understand multiple linear regressionJC Wang (WMU) Stat2160 S2160, Chapter 11 2 / 53Simple Linear Regression SLR: Housing Data ExampleGoal and Objectivesof Chapter 11Goal: To learn about regression modelingObjectivesTo learn hypotheses testing methodology for the slopeTo understand simple linear regressionTo understand multiple linear regressionJC Wang (WMU) Stat2160 S2160, Chapter 11 2 / 53Simple Linear Regression SLR: Housing Data ExampleGoal and Objectivesof Chapter 11Goal: To learn about regression modelingObjectivesTo learn hypotheses testing methodology for the slopeTo understand simple linear regressionTo understand multiple linear regressionJC Wang (WMU) Stat2160 S2160, Chapter 11 2 / 53Simple Linear Regression SLR: Housing Data ExampleGoal and Objectivesof Chapter 11Goal: To learn about regression modelingObjectivesTo learn hypotheses testing methodology for the slopeTo understand simple linear regressionTo understand multiple linear regressionJC Wang (WMU) Stat2160 S2160, Chapter 11 2 / 53Simple Linear Regression SLR: Housing Data ExampleGoal and Objectivesof Chapter 11Goal: To learn about regression modelingObjectivesTo learn hypotheses testing methodology for the slopeTo understand simple linear regressionTo understand multiple linear regressionJC Wang (WMU) Stat2160 S2160, Chapter 11 2 / 53Simple Linear Regression SLR: Housing Data ExampleOutline1Simple Linear RegressionSimple Linear Regression ModelingThings to Considered for SLRLeast Square Solution of the Fitted LineMore Regression Summary StatisticsStatistical Inference in SLR2SLR: Housing Data ExampleData and Summary StatisticsSLRJC Wang (WMU) Stat2160 S2160, Chapter 11 3 / 53Simple Linear Regression SLR: Housing Data ExampleOutline1Simple Linear RegressionSimple Linear Regression ModelingThings to Considered for SLRLeast Square Solution of the Fitted LineMore Regression Summary StatisticsStatistical Inference in SLR2SLR: Housing Data ExampleData and Summary StatisticsSLRJC Wang (WMU) Stat2160 S2160, Chapter 11 4 / 53Simple Linear Regression SLR: Housing Data ExampleSimple Linear Regression ModelingPurpose of regression analysis is predictionModel: y = b0+ b1x; where b1is the slope, y is the dependentvariable and x is the independent variable.Correlation coefficient, r.Coefficient of determination, R2(= r2in simple linear regression).JC Wang (WMU) Stat2160 S2160, Chapter 11 5 / 53Simple Linear Regression SLR: Housing Data ExampleSimple Linear Regression ModelingPurpose of regression analysis is predictionModel: y = b0+ b1x; where b1is the slope, y is the dependentvariable and x is the independent variable.Correlation coefficient, r.Coefficient of determination, R2(= r2in simple linear regression).JC Wang (WMU) Stat2160 S2160, Chapter 11 5 / 53Simple Linear Regression SLR: Housing Data ExampleSimple Linear Regression ModelingPurpose of regression analysis is predictionModel: y = b0+ b1x; where b1is the slope, y is the dependentvariable and x is the independent variable.Correlation coefficient, r.Coefficient of determination, R2(= r2in simple linear regression).JC Wang (WMU) Stat2160 S2160, Chapter 11 5 / 53Simple Linear Regression SLR: Housing Data ExampleSimple Linear Regression ModelingPurpose of regression analysis is predictionModel: y = b0+ b1x; where b1is the slope, y is the dependentvariable and x is the independent variable.Correlation coefficient, r.Coefficient of determination, R2(= r2in simple linear regression).JC Wang (WMU) Stat2160 S2160, Chapter 11 5 / 53Simple Linear Regression SLR: Housing Data ExampleSimple Linear Regression ModelingcontinuedStandard error of the estimated regression line, s.Testing hypothesis of slope, p-value.Confidence interval for slope.Residual calculation.JC Wang (WMU) Stat2160 S2160, Chapter 11 6 / 53Simple Linear Regression SLR: Housing Data ExampleSimple Linear Regression ModelingcontinuedStandard error of the estimated regression line, s.Testing hypothesis of slope, p-value.Confidence interval for slope.Residual calculation.JC Wang (WMU) Stat2160 S2160, Chapter 11 6 / 53Simple Linear Regression SLR: Housing Data ExampleSimple Linear Regression ModelingcontinuedStandard error of the estimated regression line, s.Testing hypothesis of slope, p-value.Confidence interval for slope.Residual calculation.JC Wang (WMU) Stat2160 S2160, Chapter 11 6 / 53Simple Linear Regression SLR: Housing Data ExampleSimple Linear Regression ModelingcontinuedStandard error of the estimated regression line, s.Testing hypothesis of slope, p-value.Confidence interval for slope.Residual calculation.JC Wang (WMU) Stat2160 S2160, Chapter 11 6 / 53Simple Linear Regression SLR: Housing Data ExampleSimple Linear Regression ModelingCustomer Bill and Tip ExampleBusiness students want to predict the average customer tip from anaverage customer’s restaurant bill. They have collected data from fivecustomers. The results are listed below:Customer Bill Tip1 98.84 14.562 33.46 3.773 63.60 9.814 50.68 8.915 107.34 17.33JC Wang (WMU) Stat2160 S2160, Chapter 11 7 / 53Simple Linear Regression SLR: Housing Data ExampleIssues for SLRScatter plot of dataCorrelationSLR equation, R2, confidence interval of slope, and residualsJC Wang (WMU) Stat2160 S2160, Chapter 11 8 / 53Simple Linear Regression SLR: Housing Data ExampleIssues for SLRScatter plot of dataCorrelationSLR equation, R2, confidence interval of slope, and residualsJC Wang (WMU) Stat2160 S2160, Chapter 11 8 / 53Simple Linear Regression SLR: Housing Data ExampleIssues for SLRScatter plot of dataCorrelationSLR equation, R2, confidence interval of slope, and residualsJC Wang (WMU) Stat2160 S2160, Chapter 11 8 / 53Simple Linear Regression SLR: Housing Data ExampleIdentify the Variables in SLRWe must identify the independent variable x and the dependentvariable y. What are we trying to predict? And from what we are tryingto predict.Note this story