1. Statistics 200b. Chapter 5. Chapter 4: inference via likelihood now Chapter 5: applications to particular situations

2. annual max sea levels 1931-81 Y: max cm x: year

3. 5.1 Straight-line regression. How one variable depends on others Response, Y, random Explanatories, x, fixed (covariates)

4. Reparametrize. Simplifies several things

5. Likelihood analysis.

7. Distributions.  j : IN(0,  2 ) Linear combinations of normals

9. Venice sea level. n = 51

10. Prediction. at x +

12. Example.

13. annual max sea levels 1931-81 Y: max cm x: year

14. (Raw) residuals.

16. Stat 200b. Chapter 8. Linear regression models.

17. n by 1, n by 2, 2 by 1, n by 1

19. 13 by 5

23. Effect of increasing seat height is 2  1

24. Some matrix review transpose multiplication inverse derivatives

25. Normal linear model. Estimation

26. Profile log likelihood

27. Straight-line/simple regression.

29. Fitted values. NB. Assuming matrix inverse exists

30. Weighted least squares. inverse existing

31. Example 8.8. Cycling data

34. Example 8.10. Maize data.

35. Likelihood quantities.

36. Take expected values

38. Normal distribution theory. Full rank case

39. A useful decomposition.

40. Confidence interval.

41. Gauss-Markov Theorem. page 374

42. There is a generalized inverse variant Example.

43. Eg. Teaching methods data, p. 427 Method average Usual 17 14 24 20 24 … 24 19.67 Praised 28 30 29 24 27 … 23 27.41 two-sample model / one-way layout

45. Robust/resistant estimators outlier - observation that is unusual compared to others resistant statistic - not strongly affected by outliers robust estimate - performs well under a range of potential models centered at an ideal model

51. 13 by 5

57. ANOVA table

58. 13 by 5

61. Model 1: y ~ 1 Model 2: y ~ x1 Model 3: y ~ x1 + x2 Model 4: y ~ x1 + x2 + x3 Model 5: y ~ x1 + x2 + x3 + x4 Res.Df RSS Df Sum of Sq F Pr(>F) 1 12 2715.76 2 11 1265.69 1 1450.08 242.3679 2.888e-07 *** 3 10 57.90 1 1207.78 201.8705 5.863e-07 *** 4 9 48.11 1 9.79 1.6370 0.2366 5 8 47.86 1 0.25 0.0413 0.8441 Model 1: y ~ 1 Model 2: y ~ x4 Model 3: y ~ x4 + x3 Model 4: y ~ x4 + x3 + x2 Model 5: y ~ x4 + x3 + x2 + x1 Res.Df RSS Df Sum of Sq F Pr(>F) 1 12 2715.76 2 11 883.87 1 1831.90 306.1859 1.161e-07 *** 3 10 175.74 1 708.13 118.3577 4.509e-06 *** 4 9 73.81 1 101.92 17.0356 0.00331 ** 5 8 47.86 1 25.95 4.3375 0.07082