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3. Where are we? Regression Example Exam 2 vs Final Least Squares Regression Line: SSTO = 1300 SSE = 272.1 Exam 2336544646040 Final538078938858

4. The Square of the Correlation r 2 r 2 is always between _________________ Measure total variation in responses as: r 2 = =proportion of total variability in responses that can be explained by the linear relationship with the explanatory variable x. SSTO =

5. Measuring Strength and Direction for Exam 2 vs Final pg 190 SSTO = SSE = Interpretation: We have that ___________% of the variation in _________________can be accounted for by its linear relationship with __________________. Correlation coefficient r = ___________________

6. Cautions about Correlation and Regression Read pages 134 – 136 and 152 – 159 for good examples/ discussion on following topics: Nonlinear relationships Detecting Outliers and their influence on regression results Dangers of Extrapolation (predicting outside the range of your data)

7. Cautions about Correlation and Regression Dangers of combining groups inappropriately (Simpson’s Paradox) Correlation does not prove causation

8. SPSS Regression Analysis for Exam 2 vs Final pg 191

9. SPSS Regression Analysis for Exam 2 vs Final

11. This will be an important p-value Keep this p-value of 0.018 in mind for your one clicker question …

12. Suppose p-value = 0.018. For which significance levels would the result be statistically significant? Choose all that apply... A) 0.01 B) 0.05 C) 0.10 D) Can’t tell

13. 4.Paired or Independent? a.Wish to estimate difference in highway versus city average gas mileage for 2010 cars with automatic transmissions. A random sample of 8 such cars is used and the highway and the city gas mileage is measured … … to create a CI estimate for the population mean difference between highway and city gas mileage for all 2010 cars. A.Paired B.Independent

14. 4.Paired or Independent? b.Study to compare two insurance companies on length of stay for pediatric asthma patients. A sample of 300 such cases from Insurer A was selected and a sample of 300 such cases from Insurer B was selected. Length of stay for all 600 cases recorded and used to test if the average length of stay for Insurer A pediatric asthma patients was significantly different from that for Insurer B pediatric asthma patients. A.Paired B.Independent

15. 5. Study on service time at Josh’s… is the average time less than 15 minutes? n = 100 service times Assume service times are r.s. from approx normal population. Use 5% significance level. a.State the hypotheses … H 0 : _____________________________ H a : _____________________________

16. 5. Study on service time at Josh’s… b.Sample mean is 14 min and standard error of mean is 0.5 min. Compute test statistic (include symbol and value).

17. 5. Study on service time at Josh’s… c.Find p-value … show all work.

18. d. Appropriate decision & conclusion? A. Reject H 0, there is insufficient evidence to demonstrate the service time is less than 15 minutes on average. B. Reject H 0, the mean service time is significantly less than 15 minutes. C. Fail to reject H 0, there is insufficient evidence to demonstrate the service time is less than 15 minutes on average. D. Fail to reject H 0, the mean service time is significantly less than 15 minutes.

19. 6. Defects – Study to compare defective rates for two machines. 90% CI for differ in popul defect rates (Mach 1 less Mach 2) is (0.01, 0.03). A. The p-value is more than 10%. B. The p-value is less than or equal to 10%. C. There is not enough information to know what the p-value would be. a.Based on CI, what can be said about p-value for testing for a significant difference in defective rates at 10% level? Select one:

20. 6. Defects – Study to compare defective rates for two machines. 90% CI for differ in popul defect rates (Mach 1 less Mach 2) is (0.01, 0.03). b.Complete the sentence: For this study, the sample proportion of defectives for Machine 1 was _______ % higher than that for Machine 2.