1 / 37

Regression II

Regression II. OK. OK. Non-normal. OK. Non-normal. Non-linear. OK. Non-normal. Unequal variance. Non-linear. 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:

avariella
Download Presentation

Regression II

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Regression II

  2. OK

  3. OK Non-normal

  4. OK Non-normal Non-linear

  5. OK Non-normal Unequal variance Non-linear

  6. 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

  7. Non-linear regression

  8. Non-linear regression Complex; goes through all the data points Simpler; still provides good fit to the data

  9. Non-linear regression • Three types of non-linear regression: • Quadratic regression • Smoothing • Logistic regression

  10. Quadratic regression • Y = a + bX + cX2 • Fits a parabolic curve to predict Y from X • Often fitted using least-squares - minimize MSresiduals

  11. Quadratic regression

  12. Quadratic regression c > 0 c < 0

  13. Quadratic regression • Y = a + bX + cX2 • Three parameters to estimate from the data: a, b, and c • More complex model • Requires more data to get a good fit

  14. 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

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

  16. LD50

  17. 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:

  18. 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:

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

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

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

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

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

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

  25. 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

  26. 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

  27. 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” • Factuality B. Statistics C. Truthiness D. Hypothesis

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

  29. 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

  30. 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%

  31. 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

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

More Related