a= b= WARM - UP Variable Coef StDev T P The following Regression analysis indicates the association between the number of hours you spend at the mall and the amount of money you have. Use the analysis to predict the amount of money you have from the number of hours at the mall. Regression Analysis Variable Coef StDev T P Constant 103.561 1.948 30.43 0.000 Hours -8.0756 0.2373 -10.12 0.000 S = 12.196 R-Sq = 94.7% R-Sq(adj) = 97.1% a= b= Find the Least Square Regression Line and interpret slope and y-intercept. 2. Find and interpret the Correlation. Very Strong, Negative, Linear Association

Making Predictions The following Regression analysis depicts the relationship between the Difference between Men and Women’s Ages at the time of Marriage with the Year they were married.

Making Predictions Predict the average age difference between M-W for: 1900 ? 2100 ?

Chapter 9 – Regression Analysis Errors Linear models give a predicted value for values in its data’s Range only. We cannot assume that a linear relationship in the data exists beyond the range of the data. Using values of x beyond the range of the data is not good, such a prediction is called an Extrapolation.

Chapter 9 – Regression Analysis Errors There is no way to be sure that a lurking variable is not the cause of any apparent association. A Lurking Variable is a third variable that may have an impact on the explanatory, response or both variables.

Lurking Variables and Causation The following scatterplot shows that the average life expectancy for a country is related to the number of doctors per person in that country This new scatterplot shows that the average life expectancy for a country is related to the number of televisions per person in that country:

http://tylervigen.com/

Association does not imply Causation.

Chapter 9 – Regression Analysis Errors Using Summary Statistics to do regression Analysis will not give you a TRUE model of the relationship. These scatterplots show less variation than what there really is.

Page 213: 1,2, 8-10

6. Tropical storms in the Pacific Ocean with sustained winds that exceed 74 miles per hour are called typhoons. Graph A below displays the number of recorded typhoons in two regions of the Pacific Ocean—the Eastern Pacific and the Western Pacific—for the years from 1997 to 2010. Compare the distributions of yearly frequencies of typhoons for the two regions of the Pacific Ocean for the years from 1997 to 2010.

(e) Consider graph B. i) What information is more apparent from the plots of the 4-year moving averages than from the plots of the yearly frequencies of typhoons? ii) What information is less apparent from the plots of the 4-year moving averages than from the plots of the yearly frequencies of typhoons?

What was the actual age difference in 1975?