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H-SC MATH 121 - Lecture 48 - Residual Analysis

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Homework ReviewIntroductionResidual AnalysisNonlinear RegressionOutliers and Influential PointsAssignmentResidualAnalysis andOutliersRobb T.KoetherHomeworkReviewIntroductionResidualAnalysisNonlinearRegressionOutliers andInfluentialPointsAssignmentResidual Analysis and OutliersLecture 48Sections 13.4 - 13.5Robb T. KoetherHampden-Sydney CollegeMon, Dec 1, 2008ResidualAnalysis andOutliersRobb T.KoetherHomeworkReviewIntroductionResidualAnalysisNonlinearRegressionOutliers andInfluentialPointsAssignmentOutline1Homework Review2Introduction3Residual Analysis4Nonlinear Regression5Outliers and Influential Points6AssignmentResidualAnalysis andOutliersRobb T.KoetherHomeworkReviewIntroductionResidualAnalysisNonlinearRegressionOutliers andInfluentialPointsAssignmentHomework ReviewExercise 13.4, page 821.The following data represent trends in cigaretteconsumption per capita (in hundreds) and lung cancermortality (per 100,000) for Canadian males:Cigarette Consumption (x) 11.8 12.5 15.7 19.2 21.9 23.3Mortality Rate (y) 10.4 16.5 22.9 26.6 33.8 42.8(b) Give the equation of the least squares regression line ofy = mortality rate on x = cigarette consumption.(c) Interpret the slope of the regression line. (Be specific.)(d) Use the least squares regression equation to predict thelung cancer mortality rate when the cigaretteconsumption per capita is 2000.ResidualAnalysis andOutliersRobb T.KoetherHomeworkReviewIntroductionResidualAnalysisNonlinearRegressionOutliers andInfluentialPointsAssignmentHomework ReviewSolution(b) Enter the x values into list L1and the y values into L2.Then use LinReg(a+bx) L1,L2,Y1to get theregression line.The line isˆy = −15.474 + 2.35x.ResidualAnalysis andOutliersRobb T.KoetherHomeworkReviewIntroductionResidualAnalysisNonlinearRegressionOutliers andInfluentialPointsAssignmentHomework ReviewSolution(c) The slope, 2.35, means that if x increases by 1, then yincreases by 2.35. That is, the mortality rate increasesby 2.35 deaths per 100,000 for every additional 100cigarettes consumed.(d) If cigarette consumption were 2000, the model predictsthat the mortality rate would beˆy(20) = −15.474 + 2.35(20) = 31.6lung cancer deaths per 100,000.ResidualAnalysis andOutliersRobb T.KoetherHomeworkReviewIntroductionResidualAnalysisNonlinearRegressionOutliers andInfluentialPointsAssignmentIntroductionHow do we know that a linear regression model is thebest choice?What other types of regression are there?There are many other types.How many would you like?The linear model is by far the simplest, but it is not theonly choice.ResidualAnalysis andOutliersRobb T.KoetherHomeworkReviewIntroductionResidualAnalysisNonlinearRegressionOutliers andInfluentialPointsAssignmentIntroductionHow do we know that a linear regression model is thebest choice?What other types of regression are there?There are many other types.How many would you like?The linear model is by far the simplest, but it is not theonly choice.ResidualAnalysis andOutliersRobb T.KoetherHomeworkReviewIntroductionResidualAnalysisNonlinearRegressionOutliers andInfluentialPointsAssignmentIntroductionHow do we know that a linear regression model is thebest choice?What other types of regression are there?There are many other types.How many would you like?The linear model is by far the simplest, but it is not theonly choice.ResidualAnalysis andOutliersRobb T.KoetherHomeworkReviewIntroductionResidualAnalysisNonlinearRegressionOutliers andInfluentialPointsAssignmentIntroductionHow do we know that a linear regression model is thebest choice?What other types of regression are there?There are many other types.How many would you like?The linear model is by far the simplest, but it is not theonly choice.ResidualAnalysis andOutliersRobb T.KoetherHomeworkReviewIntroductionResidualAnalysisNonlinearRegressionOutliers andInfluentialPointsAssignmentIntroductionHow do we know that a linear regression model is thebest choice?What other types of regression are there?There are many other types.How many would you like?The linear model is by far the simplest, but it is not theonly choice.ResidualAnalysis andOutliersRobb T.KoetherHomeworkReviewIntroductionResidualAnalysisNonlinearRegressionOutliers andInfluentialPointsAssignmentThe Appropriateness of the Linear ModelWe can learn a bit about the nature of the model byexamining the residuals.This is called residual analysis.First, we need to find the residualsei= yi− ˆyi.ResidualAnalysis andOutliersRobb T.KoetherHomeworkReviewIntroductionResidualAnalysisNonlinearRegressionOutliers andInfluentialPointsAssignmentThe Appropriateness of the Linear ModelTo do this on the TI-83, after finding the equation of theregression line, enterL2-Y1(L1)→L3to store the residuals in L3.Then draw a scatterplot of x versus e, that is, L1versusL3.ResidualAnalysis andOutliersRobb T.KoetherHomeworkReviewIntroductionResidualAnalysisNonlinearRegressionOutliers andInfluentialPointsAssignmentThe Residual PlotExample (Residual Plots)Free lunch rate vs. graduation rateFree Lunch RateGraduation Rate10 20 30 6050400 70 80405060708090ResidualAnalysis andOutliersRobb T.KoetherHomeworkReviewIntroductionResidualAnalysisNonlinearRegressionOutliers andInfluentialPointsAssignmentThe Residual PlotExample (Residual Plots)Free lunch rate vs. graduation rateFree Lunch RateGraduation Rate10 20 30 6050400 70 80405060708090ResidualAnalysis andOutliersRobb T.KoetherHomeworkReviewIntroductionResidualAnalysisNonlinearRegressionOutliers andInfluentialPointsAssignmentThe Residual PlotExample (Residual Plots)The residual plotFree Lunch RateResiduals10 20 30 605040 70 80-20-1001020ResidualAnalysis andOutliersRobb T.KoetherHomeworkReviewIntroductionResidualAnalysisNonlinearRegressionOutliers andInfluentialPointsAssignmentThe Appropriateness of the Linear ModelIf the residual plot shows no clear pattern, but just a bigblob of points, then the linear model is appropriate.On the other hand, if the residual plot shows a distinctcurvature, then the linear model may not beappropriate.ResidualAnalysis andOutliersRobb T.KoetherHomeworkReviewIntroductionResidualAnalysisNonlinearRegressionOutliers andInfluentialPointsAssignmentA Nonlinear ModelExample (A Nonlinear Model)Consider the following data.x y x y1 2 5 122 2 6 92 4 6 122 4 7 72 5 7 93 7 7 113 8 8 94 9 8 104 10ResidualAnalysis andOutliersRobb T.KoetherHomeworkReviewIntroductionResidualAnalysisNonlinearRegressionOutliers andInfluentialPointsAssignmentA Nonlinear ModelExample (A Nonlinear Model)The scatterplot1 2 3


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H-SC MATH 121 - Lecture 48 - Residual Analysis

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