1Chapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.Chapter 7 Scatterplots, Association, and CorrelationChapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.2Univariate vs. Bivariate Data What do we mean by “univariate” data? Are timeplots graphical displays of univariate data? What is a “Scatterplot”?Chapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.3Things to Look For in Scatterplots Direction Form Strength Unusual featuresChapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.4Direction Positive, negative, or neither?Chapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.5Form Approximately a straight line, or something else?Chapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.6Form (cont.)xy So, what if the relationship is not “linear”?xyChapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.7 Examples of “strong” relationships:StrengthxyxyxyChapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.8Strength (cont.)xy Example of a “weak” relationship:Chapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.9Unusual Features - Outliers How would you describe this person?Chapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.10Unusual 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 1213Copyright © 2009 Pearson Education, Inc.11 Dots are Supplier A and plus-signs are Supplier B. What is your conclusion?Unusual Features – Clusters or Subgroups (Cont.)Chapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.12Measuring the Strength of a Linear Relationship The correlation coefficient (r):1xyzzrnFormula from your textbook: Other formulas:22)()())((yyxxyyxxriiiiTypically, software is used to calculate r.Chapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.13 Data collected from students in college class included their heights (in inches) and weights (in pounds):Correlation ExampleChapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.14Correlation Example (cont.) For the students’ heights and weights, the correlation is r = 0.644. What does this mean in terms of strength?Chapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.15Correlation 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 1213Copyright © 2009 Pearson Education, Inc.16Sketch of Strong Non-Linear Associationr =Chapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.17Correlation Conditions Before you use correlation, you must check several conditions: Quantitative Variables Condition Straight Enough Condition Outlier ConditionChapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.18Quantitative Variables Condition How does one check this condition?Chapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.19Straight Enough Condition For these data, r is approximately zero. Does that mean there is no relationship between Baking Temp and Taste Score?Chapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.20Outlier 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 1213Copyright © 2009 Pearson Education, Inc.21Sketch of Outlier Making a Weak Correlation Look Strongwithout outlier r=with outlier r=Chapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.22Sketch of Outlier Making a Strong Correlation Look Weakwithout outlier r=with outlier r=Chapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.23Sketch of Outlier Making a Positive Correlation Look Negativewithout outlier r=with outlier r=Chapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.24Correlation 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 1213Copyright © 2009 Pearson Education, Inc.25Correlation 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 1213Copyright © 2009 Pearson Education, Inc.26Correlation MatrixChapter07 Presentation 1213Copyright © 2009 Pearson Education, Inc.27How 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 1213Copyright © 2009 Pearson Education, Inc.28Correlations 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 1213Copyright © 2009 Pearson Education, Inc.29Interpreting the Significance Probability The Signif. Prob is a “p-value”. For most applications, if this p-value falls below0.05, 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 1213Copyright © 2009 Pearson Education, Inc.30Interpreting the Significance Probability (Cont.) With larger data sets, lower values of r can still indicate “statistically significant” linear
View Full Document
Unlocking...