1. Regression II

3. OK

4. Non-normal OK

5. Non-normal OK Non-linear

6. Non-normal OK Non-linear Unequal variance

7. Non-linear regression There are nearly unlimited options here Keep it simple! Only use a particular non-linear fit if the data strongly suggest it I’ll discuss three types: –Quadratic regression –Smoothing –Logistic regression

8. Non-linear regression

9. Complex; goes through all the data points Simpler; still provides good fit to the data

10. Non-linear regression Three types of non-linear regression: –Quadratic regression –Smoothing –Logistic regression

11. Quadratic regression Y = a + bX + cX 2 Fits a parabolic curve to predict Y from X Often fitted using least-squares - minimize MS residuals

12. Quadratic regression

13. c > 0 c < 0

14. Quadratic regression Y = a + bX + cX 2 Three parameters to estimate from the data: a, b, and c More complex model Requires more data to get a good fit

15. Smoothing Runs a line (without any formula) through the data Can curve, or be straight – depends on data Several types: kernel, spline, lowess Each has a smoothing parameter to determine how much the line bends

17. Logistic Regression Used when Y is discrete – either 0 or 1 Example: survival Predicts the odds of success for Y against X

19. LD 50

20. Quick Reference Summary: Confidence Interval for Regression Slope What is it for? Estimating the slope of the linear equation Y =  +  X between an explanatory variable X and a response variable Y What does it assume? Relationship between X and Y is linear; each Y at a given X is a random sample from a normal distribution with equal variance Parameter:  Estimate: b Degrees of freedom: n-2 Formulae:

22. Quick Reference Summary: t-test for Regression Slope What is it for? To test the null hypothesis that the population parameter  equals a null hypothesized value, usually 0 What does it assume? Same as regression slope C.I. Test statistic: t Null distribution: t with n-2 d.f. Formula:

23. Sample Test statistic Null hypothesis  =0 compare How unusual is this test statistic? P < 0.05 P > 0.05 Reject H o Fail to reject H o T-test for Regression Slope Null distribution t with n-2 df

24. Class Activity Are taller people smarter, or dumber, than short people in this class? Trivia quiz, followed by group calculation

25. Trivia quiz Get out blank piece of paper Number from 1-10 Answer each multiple choice question

26. Question 1 Which of the following has the longest recorded life span? A. Termite B. Indian elephant C. Freshwater oyster D. Chimpanzee

27. Question 2 What was the first genetically engineered organism? A. Corn B. Mouse C. Sheep D. Tobacco

28. Question 3 What animal has the highest blood pressure? A. Giraffe B. Blue whale C. Elephant D. Flea

29. Question 4 What happens to the critical value of a Chi- squared distribution (with constant  ) as you increase the degrees of freedom? A. Increases B. Decreases C. Stays the same D. None of the above

30. Question 5 In the TV show The Simpsons, what is the name of Springfield Elementary`s Lunchlady? A. Lurleen B. Mary C. Ashley D. Doris

31. Question 6 Which of the following means: “the quality by which a person claims to know something intuitively, instinctively, or from the gut without regard to evidence, logic, intellectual examination, or actual facts” A.Factuality B. Statistics C. Truthiness D. Hypothesis

32. Question 7 Who invented the ANOVA? A. Dr. Harmon B. Karl Pearson C. R. A. Fisher D. Kareem Abdul-Jabar

33. Question 8 An experiment that investigates all treatment combinations of two or more variables is called a(n): A. Randomized block design B. Kruskal-Wallace design C. Factorial design D. Interaction

34. Question 9 After class one day, Shelly comes home and decides to make chocolate chip cookies. The bag she uses contains 200 chocolate chips, and she ends up making 20 cookies, which gives an average of 10 chips per cookie. She wants that first one she (randomly) chooses to be the perfect cookie--what is the likelihood that that first cookie will have at least 13 chocolate chips? A. About 5% B. About 30% C. About 10% D. About 20%

35. Question 10 Which of the following is NOT an assumption of linear regression? A. Relationship between X and Y is linear B. Each Y at a given X is a random sample C. Equal variance at each Y D. X is drawn from a normal distribution

36. Now, use your data Test the following null hypothesis: H o : The slope of the relationship between height (X) and score on the trivia quiz (Y) is zero (  =0)