Chapter 6 Scatterplots Association and Correlation Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 1 6 1 Scatterplots Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 2 Univariate vs Bivariate Data What do we mean by univariate data Are timeplots graphical displays of univariate data What is a Scatterplot Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 3 Things to Look For in Scatterplots Direction Form Strength Unusual features Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 4 Direction Positive negative or neither Negative Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 5 Form Approximately a straight line or something else Straight Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 6 Form cont y So what if the relationship is not linear Expositional and not linear x y Not a linear relationship x Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 7 Strength Examples of strong relationships y y y x x Strong Chapter06 Presentation 0615 Strong Not linear Copyright 2014 2012 2009 Pearson Education Inc x Strong Not linear 8 Strength cont Example of a weak relationship y x Vague Cloud no relationship with x and y Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 9 Unusual Features Outliers How would you describe this person Outlier Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 10 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 0615 Copyright 2014 2012 2009 Pearson Education Inc 11 Unusual Features Clusters or Subgroups Cont Dots are Supplier A and plus signs are Supplier B What is your conclusion Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 12 6 2 Correlation Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 13 Measuring the Strength of a Linear Relationship The correlation coefficient r Formula from your textbook r zx z y Other formulas r n 1 x x y y x x y y i i 2 i 2 i Typically software is used to calculate r Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 14 Correlation Example Data collected from students in college class included their heights in inches and weights in pounds Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 15 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 0615 Copyright 2014 2012 2009 Pearson Education Inc 16 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 data Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 17 Sketch of Strong Non Linear Association r Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 18 Correlation Conditions Before you use correlation you must check several conditions Quantitative Variables Condition Straight Enough Condition No Outliers Condition Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 19 Quantitative Variables Condition How does one check this condition Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 20 Straight Enough Condition For these data r is approximately zero Does that mean there is no relationship between Baking Temp and Taste Score y taste score scale of 0 to 10 12 10 8 6 4 2 0 0 100 200 300 400 500 600 700 800 x Baking Temp Deg F Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 21 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 0615 Copyright 2014 2012 2009 Pearson Education Inc 22 Sketch of Outlier Making a Weak Correlation Look Strong without outlier r with outlier Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc r 23 Sketch of Outlier Making a Strong Correlation Look Weak without outlier r with outlier Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc r 24 Sketch of Outlier Making a Positive Correlation Look Negative without outlier r with outlier Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc r 25 6 3 Warning Correlation Causation Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 26 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 0615 Copyright 2014 2012 2009 Pearson Education Inc 27 Correlation vs Causation Example If one looks at monthly data collected over many years regarding Ice Cream Sales and Shark Attacks in the USA there is a strong positive correlation Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 28 Correlation Table aka Correlation Matrix Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 29 Chapter 6 Supplement Statistically Significant Correlations Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 30 How Far Away from Zero Should r Be To Say We Have a Strong Linear Association When r is very close to zero or very close to plus or minus one the decision regarding a weak or strong linear association is fairly straightforward For cases in between these two extremes we need a more objective means of deciding is x and y have a strong linear association Statistical software easily gives us this objective criteria Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 31 Correlations and JMP Using the instructions for JMP given in your textbook in Chapter 6 the following was produced for a small data set Chapter06 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 32 Interpreting the Significance Probability The Signif Prob is a p value For most applications if this p
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