Chapter 7 Chapter07 Presentation 1213 Scatterplots Association and Correlation Copyright 2009 Pearson Education Inc 1 Univariate vs Bivariate Data What do we mean by univariate data Are timeplots graphical displays of univariate data What is a Scatterplot Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 2 Things to Look For in Scatterplots Direction Form Strength Unusual features Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 3 Direction Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc Positive negative or neither 4 Form Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc Approximately a straight line or something else 5 Form cont y So what if the relationship is not linear x y x Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 6 Strength Examples of strong relationships x Chapter07 Presentation 1213 y y y Copyright 2009 Pearson Education Inc x x 7 Strength cont Example of a weak relationship y x Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 8 Unusual Features Outliers Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc How would you describe this person 9 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 Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 10 Unusual Features Clusters or Subgroups Cont Dots are Supplier A and plus signs are Supplier B What is your conclusion Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 11 Measuring the Strength of a Linear Relationship The correlation coefficient r Formula from your textbook r z z xy 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 Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 12 Correlation Example Data collected from students in college class included their heights in inches and weights in pounds Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 13 Correlation Example cont For the students heights and weights the correlation is r 0 644 What does this mean in terms of strength Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 14 Correlation Properties What does the sign of the correlation coefficient indicate What are possible values of the correlation coefficient What if the relationship is strong but it s not linear Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 15 Sketch of Strong Non Linear Association r Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 16 Correlation Conditions Before you use correlation you must check several conditions Quantitative Variables Condition Straight Enough Condition Outlier Condition Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 17 Quantitative Variables Condition How does one check this condition Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 18 Straight Enough Condition For these data r is approximately zero Does that mean there is no relationship between Baking Temp and Taste Score Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 19 Outlier Condition How does one check this condition What impact do outliers have on the value of r What should you do if you have outliers Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 20 Sketch of Outlier Making a Weak Correlation Look Strong without outlier r with outlier Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc r 21 Sketch of Outlier Making a Strong Correlation Look Weak without outlier r with outlier Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc r 22 Sketch of Outlier Making a Positive Correlation Look Negative without outlier r with outlier Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc r 23 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 Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 24 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 Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 25 Correlation Matrix Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 26 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 Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 27 Correlations and JMP Using the instructions for JMP given in your textbook in Chapter 7 the following was produced for a small data set Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 28 Interpreting the Significance Probability The Signif Prob is a p value For most applications if this p value falls below 0 05 we conclude that the linear relationship we are seeing is not due to pure chance The smaller this value the less likely the linear association we are seeing is due to pure chance Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 29 Interpreting the Significance Probability Cont With larger data sets lower values of r can still indicate statistically significant linear associations Chapter07 Presentation 1213 Copyright 2009 Pearson Education Inc 30
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