1 Regression Line Part II Class 24

2 Class Objective After this class, you will be able to -Evaluate Regression and Correlation Difficulties and Disasters -Analyze the difference between correlation and causation

Homework Check Assignment: Chapter 3 – Exercise 3.47, 3.48 and 3.49 Reading: Chapter 3 – p

Suggested Answer 4

Copyright ©2011 Brooks/Cole, Cengage Learning Regression and Correlation Difficulties and Disasters Extrapolating too far beyond the observed range of x values Allowing outliers to overly influence results Combining groups inappropriately Using correlation and a straight-line equation to describe curvilinear data

Use Regression Line to Predict 6 If the car sales in 2004 is 29000, what will be the car sales in 2008?

Use Regression Line to Predict 7 The car sales in 2008 will be 40000

8 What is wrong when we use the following regression line to predict the height of the Americans?.

Understand Predictions of Regression Line…continued Prediction outside the range of the available data (extrapolation) is risky.

Copyright ©2011 Brooks/Cole, Cengage Learning 10 Extrapolation Risky to use a regression equation to predict values far outside the range where the original data fell (called extrapolation). No guarantee that the relationship will continue beyond the range for which we have observed data.

Copyright ©2011 Brooks/Cole, Cengage Learning 11 Example 3.17 Height and Foot Length Regression equation uncorrected data: height corrected data: height Correlation uncorrected data: r = 0.28 corrected data: r = 0.69 Three outliers were data entry errors.

Copyright ©2011 Brooks/Cole, Cengage Learning 12 Example 3.18 Earthquakes in US Correlation all data: r = 0.26 w/o SF: r = –0.824

Copyright ©2011 Brooks/Cole, Cengage Learning 13 Example 3.19 Height and Lead Feet Scatterplot of all data: College student heights and responses to the question “What is the fastest you have ever driven a car?” Scatterplot by gender: Combining two groups led to illegitimate correlation

Copyright ©2011 Brooks/Cole, Cengage Learning 14 Example 3.20 U.S. Population Predictions Correlation: r = Regression Line: population = – (Year) Poor Prediction for Year 2030 = – (2030) or about 269 million, due to curved (not linear) pattern. Population of US (in millions) for each census year between 1790 and 2000.

Causation A research study the relationship between the number of television sets (x) per household and the life expectancy (y): Explanatory Variable = ? Response Variable = ? r = ? r 2 = ? Use one sentence to interpret r Use one sentence to interpret r 2

16 From the previous interpretations, could we conclude that there is a cause-and-effect tie between the number of television set and the length of life? Explain Why yes or why no?

Causation, Common Response and Confounding Relationships – 3 possible situations X and y has a high correlation relationship X causes y X and y has a high correlation relationship, x didn’t causes y (both x and y are affected by the common lurking variables - z ) X and y has a high correlation relationship, lurking variable z affect y as well. 17

Statistics and causation 1.A strong relationship between 2 variables does NOT always mean that changes in one variable cause changes in the other. 2.The relationship between 2 variables is often influenced by other variables lurking in the background 3.The observed relationship between 2 variables may be due to direct causation, common response, or confounding. One, two or more of these factors may be present together. 18

Copyright ©2011 Brooks/Cole, Cengage Learning Correlation Does Not Prove Causation 1.Causation 2.Confounding Factors Present 3.Explanatory and Response are both affected by other variables 4.Response variable is causing a change in the explanatory variable Interpretations of an Observed Association

Homework Assignment: Chapter 3 – Exercise 3.59, 3.60 and 3.66 Reading: Chapter 3 – p