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UT Knoxville STAT 201 - Chapter 06 Student 0615

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Slide 1Slide 2Univariate vs. Bivariate DataThings to Look For in ScatterplotsDirectionFormForm (cont.)StrengthStrength (cont.)Unusual Features - OutliersUnusual Features – Clusters or SubgroupsUnusual Features – Clusters or Subgroups (Cont.)Slide 13Measuring the Strength of a Linear RelationshipCorrelation ExampleCorrelation Example (cont.)Correlation PropertiesSketch of Strong Non-Linear AssociationCorrelation ConditionsQuantitative Variables ConditionStraight Enough ConditionNo Outliers ConditionSketch of Outlier Making a Weak Correlation Look StrongSketch of Outlier Making a Strong Correlation Look WeakSketch of Outlier Making a Positive Correlation Look NegativeSlide 26Correlation vs. CausationCorrelation vs. Causation: ExampleCorrelation Table (aka Correlation Matrix)Slide 30Slide 31Correlations and JMPInterpreting the Significance ProbabilityInterpreting the Significance Probability (Cont.)1Chapter06 Presentation 0615Copyright © 2014, 2012, 2009 Pearson Education, Inc.Chapter 6Scatterplots, Association, and Correlation2Chapter06 Presentation 0615Copyright © 2014, 2012, 2009 Pearson Education, Inc.6.1ScatterplotsChapter06 Presentation 06153Copyright © 2014, 2012, 2009 Pearson Education, Inc.Univariate vs. Bivariate DataWhat do we mean by “univariate” data?Are timeplots graphical displays of univariate data?What is a “Scatterplot”?Chapter06 Presentation 06154Copyright © 2014, 2012, 2009 Pearson Education, Inc.Things to Look For in ScatterplotsDirectionFormStrengthUnusual featuresChapter06 Presentation 06155Copyright © 2014, 2012, 2009 Pearson Education, Inc.DirectionPositive, negative, or neither?NegativeChapter06 Presentation 06156Copyright © 2014, 2012, 2009 Pearson Education, Inc.FormApproximately a straight line, or something else?StraightChapter06 Presentation 06157Copyright © 2014, 2012, 2009 Pearson Education, Inc.Form (cont.)xySo, what if the relationship is not “linear”?xyExpositional and not linear Not a linear relationshipChapter06 Presentation 06158Copyright © 2014, 2012, 2009 Pearson Education, Inc.Examples of “strong” relationships:StrengthxyxyxyStrongStrongNot linearStrongNot linearChapter06 Presentation 06159Copyright © 2014, 2012, 2009 Pearson Education, Inc.Strength (cont.)xyExample of a “weak” relationship:“Vague Cloud”- no relationship with x and yChapter06 Presentation 061510Copyright © 2014, 2012, 2009 Pearson Education, Inc.Unusual Features - OutliersHow would you describe this person?OutlierChapter06 Presentation 061511Copyright © 2014, 2012, 2009 Pearson Education, Inc.Unusual Features – Clusters or Subgroupsx = thickness (in thousandths of an inch) of glue applied to one of two surfacesy = the strength of the bond between the two surfaces (higher values mean stronger bond).Chapter06 Presentation 061512Copyright © 2014, 2012, 2009 Pearson Education, Inc.Dots are Supplier A and plus-signs are Supplier B. What is your conclusion?Unusual Features – Clusters or Subgroups (Cont.)13Chapter06 Presentation 0615Copyright © 2014, 2012, 2009 Pearson Education, Inc.6.2CorrelationChapter06 Presentation 061514Copyright © 2014, 2012, 2009 Pearson Education, Inc.Measuring the Strength of a Linear RelationshipThe correlation coefficient (r):Formula from your textbook: Other formulas:Typically, software is used to calculate r.1x yz zrn=-�22)()())((yyxxyyxxriiiiChapter06 Presentation 061515Copyright © 2014, 2012, 2009 Pearson Education, Inc.Data collected from students in college class included their heights (in inches) and weights (in pounds):Correlation ExampleChapter06 Presentation 061516Copyright © 2014, 2012, 2009 Pearson Education, Inc.Correlation Example (cont.)For the students’ heights and weights, the correlation is r = 0.644. What does this mean in terms of strength?Chapter06 Presentation 061517Copyright © 2014, 2012, 2009 Pearson Education, Inc.Correlation PropertiesWhat does the sign of the correlation coefficient indicate? Direction What are possible values of the correlation coefficient? -1 and +1 What if the relationship is strong, but it’s not linear?When r=0, only measure of linear dataChapter06 Presentation 061518Copyright © 2014, 2012, 2009 Pearson Education, Inc.Sketch of Strong Non-Linear Associationr =Chapter06 Presentation 061519Copyright © 2014, 2012, 2009 Pearson Education, Inc.Correlation ConditionsBefore you use correlation, you must check several conditions:Quantitative Variables ConditionStraight Enough ConditionNo Outliers ConditionChapter06 Presentation 061520Copyright © 2014, 2012, 2009 Pearson Education, Inc.Quantitative Variables ConditionHow does one check this condition?Chapter06 Presentation 061521Copyright © 2014, 2012, 2009 Pearson Education, Inc.Straight Enough ConditionFor these data, r is approximately zero.Does that mean there is no relationship between Baking Temp and Taste Score?0 100 200 300 400 500 600 700 800024681012x=Baking Temp (Deg. F)y=taste score(scale of 0 to 10)Chapter06 Presentation 061522Copyright © 2014, 2012, 2009 Pearson Education, Inc.No Outliers ConditionHow does one check this condition?Look at scatter plot What impact do outliers have on the value of r?May make it it look strong when it was weak vvs.What should you do if you have outliers?Chapter06 Presentation 061523Copyright © 2014, 2012, 2009 Pearson Education, Inc.Sketch of Outlier Making a Weak Correlation Look Strongwithout outlier r=with outlier r=Chapter06 Presentation 061524Copyright © 2014, 2012, 2009 Pearson Education, Inc.Sketch of Outlier Making a Strong Correlation Look Weakwithout outlier r=with outlier r=Chapter06 Presentation 061525Copyright © 2014, 2012, 2009 Pearson Education, Inc.Sketch of Outlier Making a Positive Correlation Look Negativewithout outlier r=with outlier r=26Chapter06 Presentation 0615Copyright © 2014, 2012, 2009 Pearson Education, Inc.6.3Warning: Correlation ¹ CausationChapter06 Presentation 061527Copyright © 2014, 2012, 2009 Pearson Education, Inc.Correlation vs. CausationSo, when the value of r is close to +1 or -1, does that necessarily mean changes in one variable cause changes in the other variable? Why might two variables be highly correlated, but not have a cause/effect association?Chapter06 Presentation 061528Copyright © 2014, 2012, 2009 Pearson Education, Inc.Correlation vs. Causation:


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UT Knoxville STAT 201 - Chapter 06 Student 0615

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