Statistics 100C: Linear Models
Announcements
First lecture is on Friday, 23 September 2022
Location: Dodd Hall 175
Day/time: MWF 11:00 - 11:50
See you then!
For the course syllabus click
here.
Useful links:
http://www.socr.ucla.edu
http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials
Download R and packages.
Download RStudio.
Handouts
The next five links are the statistical tables needed for the entire quarter (from "Mathematical Statistics and Data Analysis", by John Rice, Doxbury Press, Second Edition (1995)).
Table 1: Standard normal distribution table (Z).
Table 2: Chi-square distribution table.
Table 3: t distribution table.
Table 4: F distribution table (95th percentiles).
Table 5: F distribution table (99th percentiles).
1. History of regression: Francis Galton's 1886 paper.
2. Simple regression.
3. Simple regression - introduction.
4. Compare variability
around sample mean of y with variability around the fitted line.
5. Variance and covariance
operations in simple regression.
6. Simple regression - summary.
7. Effect on
simple regression when a data point is deleted.
8. Gauss-Markov theorem.
9. Hypothesis testing - class
activity.
10. Hypothesis testing - class
activity solutions.
11. Hypothesis testing in
simple regression using the full and reduced model - example in R.
12. Non-central chi-squared distribution.
13. Non-central chi-squared, t, and F distributions in R.
14. Power analysis.
15. Power analysis in simple
regression - example in R.
16. Multiple regression - two
predictors.
17. Matrix and vector
differentiation.
18. Multiple regression in R using matrix form.
19. Expectations and variance operations in
multiple regression using properties of random vectors.
20. Fitted values and their variance
covariance matrix.
21. Residuals and their variance covariance matrix.
22. Gauss-Markov
theorem in multiple regression.
23. Multivariate normal distribution.
24. Multivariate
normal distribution and distribution theory in multiple regression.
25. Partial coefficients -
example.
26. Partial regression - examples.
27. Partial coefficients - paper 1.
28. Partial coefficients - paper 2.
29. Adding an extra
predictor - paper 3.
30. Adding several
predictors - paper 4.
31. Partial regression - two
special cases.
32. Inverse of
a partitioned matrix.
33. Constrained least squares - example.
34. Canonical form and
constrained least squares - example.
35. Centering
and scaling and multicollinearity.
36. Centering and scaling - example.
37. Centering and scaling
(same as #43).
38. Comparing
regression equations.
39. Tests of Equality
Between Sets of Coefficients in Two Linear Regressions regression equations,
Econometrica, Vol. 28, No. 3 (Jul., 1960), pp. 591-605.
40. Comparing
regression equations - example 1.
41. Comparing
regression equations - example 2.
42. Impact on regression when deleting a data point.
43. Impact on regression when adding a data point.
44. Impact on regression when adding a data point - example in R.
45. Joint distributions of
functions of random variables.
46. Beta distribution.
47. Multiple regression.
Practice problems
Practice problems.
Practice
problems - solutions.
Practice 1.
Practice 1 - solutions.
Practice 2.
Practice 2 - solutions.
Exam 1 solutions.
Week 8 - practice problems.
Week 8 - practice
problems solutions.
Practice exam 2.
Practice exam 2 - solutions.
Week 9 - practice
problems.
Week 9 - practice
problems solutions.
Exam 2 solutions.
Week 10 - practice
problems.
Week 10 - practice
problems solutions.
Labs
Homework
Back to the Statistics Department
Home page.