Homework ReviewIntroductionThe True ModelLinear Regression AnalysisTesting the Significance of the RelationshipTesting the Significance on the TI-83Significance vs. Strength of the RelationshipAssignmentTheSignificance ofthe ModelRobb T.KoetherHomeworkReviewIntroductionThe TrueModelLinearRegressionAnalysisTesting theSignificanceof theRelationshipTesting theSignificanceon the TI-83Significancevs. Strengthof theRelationshipAssignmentThe Significance of the ModelLecture 47Section 13.10Robb T. KoetherHampden-Sydney CollegeTue, Nov 24, 2009TheSignificance ofthe ModelRobb T.KoetherHomeworkReviewIntroductionThe TrueModelLinearRegressionAnalysisTesting theSignificanceof theRelationshipTesting theSignificanceon the TI-83Significancevs. Strengthof theRelationshipAssignmentOutline1Homework Review2Introduction3The True Model4Linear Regression Analysis5Testing the Significance of the Relationship6Testing the Significance on the TI-837Significance vs. Strength of the Relationship8AssignmentTheSignificance ofthe ModelRobb T.KoetherHomeworkReviewIntroductionThe TrueModelLinearRegressionAnalysisTesting theSignificanceof theRelationshipTesting theSignificanceon the TI-83Significancevs. Strengthof theRelationshipAssignmentOutline1Homework Review2Introduction3The True Model4Linear Regression Analysis5Testing the Significance of the Relationship6Testing the Significance on the TI-837Significance vs. Strength of the Relationship8AssignmentTheSignificance ofthe ModelRobb T.KoetherHomeworkReviewIntroductionThe TrueModelLinearRegressionAnalysisTesting theSignificanceof theRelationshipTesting theSignificanceon the TI-83Significancevs. Strengthof theRelationshipAssignmentHomework ReviewPractice ProblemDate Crude Oil Date GasolineJan 16 40.98 Jan 19 1.833Jan 23 41.05 Jan 26 1.833Jan 30 42.07 Feb 2 1.894Feb 6 41.77 Feb 9 1.926Feb 13 43.04 Feb 16 1.970Feb 20 39.87 Feb 23 1.924Feb 27 40.22 Mar 2 1.942Mar 6 42.85 Mar 9 1.936Mar 13 42.91 Mar 16 1.921Mar 20 44.90 Mar 23 1.950Mar 27 50.10 Mar 30 2.048Apr 3 48.09 Apr 9 2.044TheSignificance ofthe ModelRobb T.KoetherHomeworkReviewIntroductionThe TrueModelLinearRegressionAnalysisTesting theSignificanceof theRelationshipTesting theSignificanceon the TI-83Significancevs. Strengthof theRelationshipAssignmentHomework ReviewPractice Problem(a) Draw the scatter plot.(b) Find the equation of the regression line.(c) Perform the residual analysis.(d) Find the correlation coefficient.(e) Find the coefficient of determination.(f) Compute SST, SSR, and SSE.TheSignificance ofthe ModelRobb T.KoetherHomeworkReviewIntroductionThe TrueModelLinearRegressionAnalysisTesting theSignificanceof theRelationshipTesting theSignificanceon the TI-83Significancevs. Strengthof theRelationshipAssignmentSolutionPractice Problem(a) The scatter plot:40 42 44 46 48 501.851.902.001.952.05TheSignificance ofthe ModelRobb T.KoetherHomeworkReviewIntroductionThe TrueModelLinearRegressionAnalysisTesting theSignificanceof theRelationshipTesting theSignificanceon the TI-83Significancevs. Strengthof theRelationshipAssignmentSolutionPractice Problem(b) Store oil prices in L1and gas prices in L2.Enter LinReg(a+bx) L1,L2,Y1and press ENTER.The equation of the regression line isˆy = 1.189 + 0.01728x.TheSignificance ofthe ModelRobb T.KoetherHomeworkReviewIntroductionThe TrueModelLinearRegressionAnalysisTesting theSignificanceof theRelationshipTesting theSignificanceon the TI-83Significancevs. Strengthof theRelationshipAssignmentSolutionPractice Problem(c) The residual plot:40 42 44 46 48 50-0.10-0.050.000.100.05There is no curvature, so a linear model is appropriate.TheSignificance ofthe ModelRobb T.KoetherHomeworkReviewIntroductionThe TrueModelLinearRegressionAnalysisTesting theSignificanceof theRelationshipTesting theSignificanceon the TI-83Significancevs. Strengthof theRelationshipAssignmentSolutionPractice Problem(d) When we did LinReg, we saw that the correlationcoefficient wasr = 0.8090.(e) The coefficient of determination isr2= 0.6545.TheSignificance ofthe ModelRobb T.KoetherHomeworkReviewIntroductionThe TrueModelLinearRegressionAnalysisTesting theSignificanceof theRelationshipTesting theSignificanceon the TI-83Significancevs. Strengthof theRelationshipAssignmentSolutionPractice Problem(e)SST = sum((L2-y)2) = 0.0490.SSR = R2SST = 0.0321.Therefore,SSE = SST − SSR= 0.0490 − 0.0321= 0.0169.TheSignificance ofthe ModelRobb T.KoetherHomeworkReviewIntroductionThe TrueModelLinearRegressionAnalysisTesting theSignificanceof theRelationshipTesting theSignificanceon the TI-83Significancevs. Strengthof theRelationshipAssignmentOutline1Homework Review2Introduction3The True Model4Linear Regression Analysis5Testing the Significance of the Relationship6Testing the Significance on the TI-837Significance vs. Strength of the Relationship8AssignmentTheSignificance ofthe ModelRobb T.KoetherHomeworkReviewIntroductionThe TrueModelLinearRegressionAnalysisTesting theSignificanceof theRelationshipTesting theSignificanceon the TI-83Significancevs. Strengthof theRelationshipAssignmentIntroductionWe finally address the question of whether therelationship between x and y is significant.If it is not significant, then any correlation we observe ispurely accidental.This is relatively likely in small samples, whererandomness dominates.In larger samples, it is not likely, but weak accidentalcorrelations are still possible.We will perform a test that will settle the question, up toa level of certainty (α).TheSignificance ofthe ModelRobb T.KoetherHomeworkReviewIntroductionThe TrueModelLinearRegressionAnalysisTesting theSignificanceof theRelationshipTesting theSignificanceon the TI-83Significancevs. Strengthof theRelationshipAssignmentIntroductionWe finally address the question of whether therelationship between x and y is significant.If it is not significant, then any correlation we observe ispurely accidental.This is relatively likely in small samples, whererandomness dominates.In larger samples, it is not likely, but weak accidentalcorrelations are still possible.We will perform a test that will settle the question, up toa level of certainty (α).TheSignificance ofthe ModelRobb T.KoetherHomeworkReviewIntroductionThe TrueModelLinearRegressionAnalysisTesting theSignificanceof theRelationshipTesting theSignificanceon the TI-83Significancevs. Strengthof theRelationshipAssignmentIntroductionWe finally address the question of whether therelationship between x and y is significant.If it is not significant, then any correlation we observe
View Full Document
Unlocking...