- Time and Place: 10:00 MWF, Fenton 105
- CRN: 33653 (Math 463) and 33667 (Math 563)
- Textbook: Classical and Modern Regression with Applications by R.H. Myers, 2nd Edition
- Reference book: Applied Linear Statistical Models by J. Neter, M.H. Kutner, C.J. Nachtsheim and W. Wasserman, Fourth Edition.
- Final Exam: 15:15 - 17:15, Wed, June 10, 104 Deady Hall
- Office Hours: 3:00 - 4:00 MWF, 1:00 - 2:00 W at Fenton 105
- Office Phone: 346-4701
Regression analysis consists of a collection of techniques used to explore and understand the relationship between variables. This course is designed to help you learn the tools needed to carry out the statistical regression analysis in a variety of applications. The emphasis is on graphical exploration, model building, estimation, inference, diagnostics and model checking.
Syllabus
Grading Policy
Your course grade is a weighted average of the following three performance scores: homework (30%), project ( 35%) and final exam (35%).
Instructions for your project!
Course Grade
Thank you for taking my class!!!
Datasets used in class :Salary , Smoking and lung cancer , Forestry , Exercise and Cholesterol , April 24 , Hospital ,
Surgical Unit Example , Population , Blood Pressure , Body Fat , Mathematics Proficiency ,
Patients , Disease Outbreak , One-way Analysis of Variance, Two-way Analysis of Variance
Quiz:
Quizzes are optional. However, solving quiz problems will help you to understand the material you have learned in the class. You can also earn extral credits if your solutions are correct.
Quiz 1 (due Friday, 4/17) and solution , Quiz 2 (due Friday, 5/1) and solution ,
Homework Assignments and Topics for the class (posted here at least 24 hours in advance)
- Mon, 3/30: Review simple linear regression, and discuss the simple regression through the origin. Read 1.1-1.3, 2.1-2.7. Homework: None
- Wed, 4/1: Analysis of variance and quality of fitted model Read 2.8, 2.12. Homework: 2.9 , 2.17 , 2.18 . (Due next Monday, 4/6)
- Fri, 4/3: Diagnostics and remedial measures.
Read 2.10. Homework:
2.14 (Due Wednesday, 4/8)
- Mon, 4/6: Simultaneous inferences. Read 2.10. Homework: 2.15 (Due Friday, 4/10)
- Wed, 4/8: Simultaneous inferences. Read 2.10. Homework: 2.16 (Due Monday, 4/13)
- Fri, 4/10: Case when $X$ is random, correlation
analysis.
Read 2.13, 3.1, 3.2 Homework: Use the data in Problem
2.15 .
(i) Test if the correlation between arm strength and dynamic lift is 0.
(ii) Find a 95% confidence interval for the correlation.
- Mon, 4/13: Introduction to multiple linear regression model. Read 3.1, 3.2, 3.3 Homework: Refer to Problem 3.11 . Consider the model y=b_0 + b_1 x_1 + b_2 x_2 +b_3 x_3 + e. (i) Use the command regression to fit the regression with the above model, (ii) Do not use the command regression , find the estimates of the regression coeffcients step by step.
- Wed, 4/15: Analysis of variance results and
inferences about regression parameters.
Read 3.3, 3.4
Homework: (Due next Monday, 4/20) Refer to homework assignment Problem 3.11 on Monday.
(a) Test whether there is a regression relation between the response variable and predictor variables. Consider four cases: (i) H_0: b_1=b_2=b_3=0 (ii) H_0: b_1=0, (iii) H_0: b_2=0, (iv) H_0: b_3=0.
(b) Find 95% confidence intervals for b_1, b_2, b_3.
(c) Find joint 95% confidence intervals for b_1, b_2, b_3 by the Bonferroni procedure.
(d) Find 95% joint confidence region for b_1, b_2, b_3 by the F-procedure.
- Fri, 4/17: Confidence intervals and joint confidence
intervals for regression coefficients and mean responses
Read 3.5, 3.7
Homework:
Problem 3.5 (a)-(c) .
- Mon, 4/20: Extra sums of squares and tests on subsets of the regression parameters Read page 95-102 Homework: I. Problem 3.5 (d) -(e) . II. Refer to Problem 3.11 , consider the model y=b_0 + b_1 ln x_1 + b_2 ln x_2 +b_3 ln x_3 + e. Find SSR(b_2, b_3 | b_1), SSR(b_2|b_3, b_1) and test H_0: b_2=b_3=0.
- Wed, 4/22: Test of the general linear hypothesis Read pp103-111. Homework: Problem 3.8 .
- Fri, 4/24:
F test for lack of fit and
multicollinearity
Read pp 116-120 and pp 123-128.
Homework: 3.9
- Mon, 4/27: Multicollinearity Read pp 128-133. Homework: 3.11
- Wed, 4/29: Polynomial and interaction regression models Read pp. 135-152. Homework: 3.20
- Fri, 5/1: Building the regression model:
overview and standard criteria for comparing models
Read Hand out and pp. 165-178.
Homework: Refer to
Problem 4.4 (a)-(b) (due Wednesday, 5/6),
Replace the model by
y=b_0+ b_1 x_1+b_2 x_2 + b_3 x_3 + b_4 x_4 + b_5 x_1^2 + b_6 x_2^2 + b_7 x_3^2 + b_8 x_4^2 +e
Solution to part (a) in the original problem
- Mon, 5/4: All-possible-regressions procedure for variables reduction. Read pp. 178- 190. Homework: Refer to Problem 4.8 (due Friday 5/8) (a), (c) Select a model uing stepwise regression with a significance level of 0.25 for entry and 0.05 for removal; (d) Select a model using backward elimination with a significance level of 0.10. Solution
- Wed, 5/6: Analysis of residuals I Read pp 209-220. Homework: Problem 5.3 (due Monday, 5/11)
- Fri, 5/8: Analysis of residuals
Read pp 209-230
Homework:
Problem 5.5
- Mon, 5/11: Identify outliers and influential cases Read pp 250-260. Homework
- Wed, 5/13: Influence diagnostics Read pp 260 -272. Homework
- Fri, 5/15: Unequal error variances remedial
measures: weighted least square
Read pp 277 - 287
Homework (Refer to
SMSA dataset ) (due Wed 5/20)
- Mon, 5/18: Multicollinearity remdial measurees: ridge regression Read pp 369 -389 Homework (due Friday 5/22)
- Wed, 5/20: Remedial measures for influential cases: robust regression Read pp 348-356 Homework (due Wednesday, 5/27)
- Fri, 5/22: Nonlinear regression I
Read pp 424-436
- Mon, 5/25: Memorial Day
- Wed, 5/27: Nonlinear regression II Read pp 436-441 Homework
- Fri, 5/29:
Logistic regression, Poisson regression
and generalized linear models
Read pp 315 -339
- Mon, 6/1: One-way analysis of variance
- Wed, 6/3: Two-way analysis of variance
- Fri, 6/5:
- Wed, 6/10: Final Exam