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 DataWhat 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 ScatterplotsDirectionFormStrengthUnusual featuresChapter06 Presentation 06155Copyright © 2014, 2012, 2009 Pearson Education, Inc.DirectionPositive, negative, or neither?NegativeChapter06 Presentation 06156Copyright © 2014, 2012, 2009 Pearson Education, Inc.FormApproximately a straight line, or something else?StraightChapter06 Presentation 06157Copyright © 2014, 2012, 2009 Pearson Education, Inc.Form (cont.)xySo, 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.)xyExample of a “weak” relationship:“Vague Cloud”- no relationship with x and yChapter06 Presentation 061510Copyright © 2014, 2012, 2009 Pearson Education, Inc.Unusual Features - OutliersHow would you describe this person?OutlierChapter06 Presentation 061511Copyright © 2014, 2012, 2009 Pearson Education, Inc.Unusual Features – Clusters or Subgroupsx = thickness (in thousandths of an inch) of glue applied to one of two surfacesy = 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 RelationshipThe 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 PropertiesWhat 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 ConditionsBefore you use correlation, you must check several conditions:Quantitative Variables ConditionStraight Enough ConditionNo Outliers ConditionChapter06 Presentation 061520Copyright © 2014, 2012, 2009 Pearson Education, Inc.Quantitative Variables ConditionHow does one check this condition?Chapter06 Presentation 061521Copyright © 2014, 2012, 2009 Pearson Education, Inc.Straight Enough ConditionFor 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 ConditionHow 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. CausationSo, 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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