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.