Math 338 & Stat 438 at Lehigh University

Math 338/Stat 438 (Regression Analysis): Least square principles in multiple regression and their interpretations; estimation, hypothesis testing, confidence interval and prediction interval; residual analysis, multicollinearity, selection of regression models; comparison of data sets, analysis of variance and covariance; simultameous inference procedures. Use of computer packages for statistical analysis. Prerequisite: Math 12 or Math 231.

Here is a typical course description of Regession Analysis at Lehigh University.

This is the home page for Spring 1996 Math 338 ( Regression Analysis ) at Lehigh University.

The text is `Regression Analysis : Concepts and Applications' by F. A. Graybill and H. K. Iyer. More information will follow later (or call me at (610) 758-3735).

Instructor: Professor Wei-Min Huang, Department of Mathematics. To contact me, send e-mail to wh02@Lehigh.EDU, or click here Mail-Me, if your web server supports forms. Click for Lehigh's home page or for Lehigh Mathematics Department home page.

For now the Homework Assignments are:

1. HW #1: Problem 1.6.1 parts (a) and (i), (Text, page 46); Exercises 1.10.5, 1.10.6, 1.10.8 (Text, page 70). Answer all questions without using MINITAB or SAS.
2. HW #2: Problems 1.10.9, 1.10.10, 1.10.11 (Text, page 71); Problems M1.6.1 - M1.6.10 (Lab Book, page 25), use MINITAB to answer these problems from the Lab Book.
3. HW #3: Show that the beta-sub-o star and beta-sub-1 star we derived from the first-derivetive equations is the solution to the Minimization based on the total squared errors between the responses and the fitted values. Use the hint I gave you in class.
4. HW #4: Textboob, 2.4.4, 6, 7, 8, 10, 12; LabM, M2.3.1, 11, 12, 14, 15. (Don't us Simple Linear Regression Model yet in solving these problems.)
5. HW #5: Refer to Task 3.4.1 and crystal.dat on page 118 in the Textbook. (1) Use MINITAB to verify numerically the values of SXY, SSX, MSE, and the LS estimates of beta-o and beta-1. (2) (a) Use MINITAB matrix and vector (column) operations to verify the LS estimate of the beta-vector. (b) Find the estimated values of y-sub-i and the residuals. Also show that (using MINITAB) sum of residuals is zero and sum of residuals*x-sub-i is also zero. (3) (a) Obtain a scater-plot of the pairs (x-sub-i, y-sub-i), for i=1,...,14. Then super-impose the estimated points (x-sub-i, y-estimated-i) on the same plot. Use "mplot" in MINITAB. (b) Find the correlation coefficient of (x-sub-i, y-sub-i), i=1,...,14. Summarize your findings from (a) and (b). (See handout for details of this HW assignment.)
6. HW #6: Problems 3.12.3 (page 215, Text, refer to chol.dat); Problem 3.12.4 (omit part (e)).
7. HW #7: See the instructor.
8. HW #8: Problem 4.12.1 (Textbook, page 335); Read Chapters 3 and 4 in the Lab Book and do problems M3.5.1,2,3 also obtain the residual plots using (a) ordinary residuals and (b) standardized residuals.
9. HW #9: (1) M3.6.5,6,8,10,11 (Lab Manual, page 62); (2) M3.7.2, page 65; (3) (Refer to Bodyfat.dat in the handout). For testing Ho : beta1 + 2*beta3 = 0.1 show numerically that t^2 = F where t = (beta1-hat + 2*beta3-hat - 0.1) / SE(beta1-hat + 2*beta3-hat) and F = [ (SSE(reduced)-SSE(full))/(df(reduced)-df(full) ] / [ SSE(full)/df(full) ].
10. HW #10: (1) Problem 4.12.2, Textbook, page 337. Don't use MINITAB's MACROS for this problem; (2) M4.11.1, Lab Manual, page 100. Use MINITAB's MACROS to answer this problem.
11. HW #11: (1) Problem 3.6.4 (c), Textbook; (2) Problem 4.12.3 (a)-(g).
12. HW #12: (1) Problem 1 from the Handout on "One-Way ANOVA and Multiple Linear Regression"; (2) Analyze the Ski Resort Data (ski.dat). Especially determine 3 ANOVA Tables and 3 F-tests for models using (a) X1 alone (b) X2 alone, and (c) both X1 and X2. Discuss your findings.
13. HW #13: Two problems, see Handout.
14. HW #14: (1) Exercise 5.6.1 , Textbook, pages 399-402; (2) Refer to Hospital Data (hospital.dat). (a) Find the correlation coefficient matrix of the 3 regressors X1, X2, and X3. (b) Find the condition indices and the condition number of the matrix in (a). Discuss the results; (3) Refer to Hospital Data. Find the Cook's distances and the studentized deleted residuals. Determine all the possible influential observations or possible outliers.
15. HW #15: Refer to Hospital Data Set (hospital.dat). (a) Use ridge regression to estimate the regression coefficients. Use delta (the shrinkage or biasing parameter) on the basis of the stability of the estimated regression coefficients; (b) Obtain the regression line using all 30 observations. Also list the COOK, studentized deleted residuals and DFFITS. Then identify all possible influential observations and outliers; (c) Obtain the regression line using 29 observations (with #30 deleted). Also list the COOK, studentized deleted residuals and DFFITS. Then identify all possible influential observations and outliers.
16. HW #16: Refer to Hospital Data Set. (1) Perform all-subsets regression and determine the best possible subset. (2) Perform forward-regression and determine the best possible combination of regressors. (3) Perform the principal component analysis and then eliminate the necessary components (using t-test). Based on the remaining components to back estimate the coefficients of the original regression model.