Math 483/583 Linear Statistical Models Summer, 2006
Meetings: MWR 10:50-1:30, Engr 105 on MW, Engr 107 on R
Instructor: Greg Morrow
Office: EN 271, (719) 262 –3184, gmorrow@uccs.edu
Hours: MWR 10:15-10:45, MR: 1:45 -2:30, and W: 1:45-2:00.
Prerequisite: Linear Algebra and a first course in Statistics.
Text: Introduction to Linear Regression Analysis, 3rd ed. (2001), by D.C. Montgomery, E.A. Peck, and C.G. Vining.
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Description:
Statistical modeling using least squares and weighted least squares approaches.
Comparisons of models will be based on computer-aided calculations. Students
will be required to use a statistical software package (computations will be
illustrated with Microsoft Excel) for doing multiple regression calculations and
producing graphics. Coverage: Chapters 2 - 4 (core theory, including the
general linear hypothesis and model adequacy checking), 5- 6 (correcting model
assumptions), 7-8 (applications), and Chapter 9 (variable selection).
Homework and Tests. The homework is a major part of the course. This will include some theory as well as numerical calculation and interpretation. Students will need to be able to use Excel or perhaps MatLab or another statistical package. The final grade will be based on: homework, 50%, mid-term exam, 25%, and final exam 25%.
Grading. 90’s = A, 80’s = B, 70’s = C.
Assignments and Due dates: Late homework will not be accepted. One homework assignment may be dropped.
Anova for Simple Linear Regression
Simulation for Simple Linear Regression
Example 2.8 Intercept vs No Intercept Models
Data Bank Website: ftp://ftp.wiley.com/public/sci_tech_med/regression_3e/
Lack of Fit Analysis for Computer Repair Time data
Example 5.1 Peak Energy Demand
Weighted Least Squares for Supervisor Data
Example 5.5 Restaurant Food Sales
Weighted Approach to Example 5.1
Exercise 5.7 Clathrate Formation Data
Diagnostic measures of leverage and influence Exercise 6.12, Wine data
Extracting the Diagonal of a Square Matrix in Excel
Example 7.2 Cubic Spline Voltage Drop data
Table 7.7 Chemical Process Conversion
Example 8.1 Tool Life and Lathe Speed
Problem 8.11 Strength of Fiber by % Cotton
Problem 8.13 Wine Quality by Flavor and Region
Calculation of Table 9.2 for Hald Cement Data via Maple
Calculation of Forward and Stepwise Regression for Hald Cement data in Excel
Problem 6.2, Influence Analysis for the Property Valuation Data
Example on the Additive Model in Two-way Anova
Example 12.2; Gauss-Newton Iteration with Puromycin data
Example 13.1 Pneumoconiosis data
DUE DATES (revised JULY 3).
HW I. Due: June 15.
2.4, 2.9, 2.13.
HW II. Due: June 19.
2.10, 2.17, 2.19 (Grad), 2.21.
HW III. Due: June 22.
3.5, 3.8, 3.15.
HW IV. Due: June 26.
4.4, 4.9, 4.14.
HW V. Due: June 29.
5.2, 5.3, 5.11.
Midterm Exam. Take home part Due: 10:50 am, July 5.
Quiz on Midterm on Thursday, July 6.
HW VI. Due: July 6.
6.2, 7.6, 7.11
HW VII. Due: July 10.
7.16, 7.18, 8.3, 8.9 (Grad).
HW VIII. Due: July 13.
9.4. (9.4part(e) is extra credit.)
NO CLASS June 17-20.
Final Exam. IN CLASS on July 24.
REVIEW for FINAL EXAM: Problems 5.10, 7.10, 7.20, 8.5, 9.4, 12.8.
Directions for 5.10. Data for problem 5.10.
Combine parts (b) and (c) else one obtains negative weights.
Fit sqrt(si)= sqrt(standard deviation) to the x1,x2,x3.
The weights are still wi= 1/si^2, so sqrt(wi)=1/si.
Analyze the residuals via residual vs. predicted plot and normal probability plot.
The following is not required but worthy of note:
Since in 5.10 we have a full factorial experiment with replications (3*( 3^3)=81 observationsw),
one may also fit interactions x1*x2,x1*x3, x2*x3 in addition to the linear terms.
This may be done in both un-weighted and weighted cases. (Keep the weights as above.)
The weighted fit has only moderate need of the interaction terms.