STAT 714: Linear Statistical Models - fa 2023

10:05 am - 11:20 am, TR, LeConte College 205, Aug 24th - Dec 18th, 2023

Instructor: Dr. Karl Gregory
Instructor office: LeConte College 216C

Course syllabus

Lecture slides Annotated Topics Corresponding section(s) of Monahan
Lec_00.pdf Lec_00_annotated.pdf Course intro
Rev_01.pdf Rev_01_annotated.pdf Vectors and matrices, matrix inverse
Rev_02.pdf Rev_02_annotated.pdf The equation Ax = b
Rev_03.pdf Rev_03_annotated.pdf Column space, null space, and rank of a matrix
Rev_04.pdf Rev_04_annotated.pdf Orthogonal subspaces, bases, and projections, orthogonal decomposition, Gram-Schmidt
Rev_05.pdf Rev_05_annotated.pdf Eigenvalues and eigenvectors, the determinant, diagonalization
Rev_06.pdf Rev_06_annotated.pdf Symmetric matrices, spectral decomposition, quadratic forms, singular value decomposition
End introductory material
Lec_01.pdf Lec_01_annotated.pdf Projection and idempotent matrices, generalized inverse, least-squares geometry Chapter 2
Lec_02.pdf Lec_02_annotated.pdf Estimability, reparameterization, conditions for unique solution, restricted model Chapter 3
End exam I material
Lec_03.pdf Lec_03_annotated.pdf Gauss-Markov model, BLUE, Aitken model, generalized least-squares Chapter 4
Lec_04.pdf Lec_04_annotated.pdf Distributions of quadratic forms, Cochran's theorem, ANOVA Chapter 5,7
Lec_05.pdf Lec_05_annotated.pdf Inference, general linear hypothesis, LRT, simultaneous confidence intervals Chapter 6
End exam II material
Lec_06.pdf Lec_06_annotated.pdf Variance component estimation in random and mixed effects models, REML Chapter 8

Homework Topics Due in class on Solutions
hw_01.pdf Matrix inverse, solving Ax = b, constructing design matrices, linear independence, orthogonality Thursday, Aug 31st hw_01_sol.pdf
hw_02.pdf Dimension of a subspace, bases, rank, orthogonal complements, orthogonal projections Thursday, Sep 14th hw_02_sol.pdf
hw_03.pdf Eigenvalues, eigenvectors, trace, determinant, quadratic forms, symmetric matrices Tuesday, Sep 26th hw_03_sol.pdf
hw_04.pdf Projections, generalized inverses, least-squares, model reparameterization Tuesday, Oct 10th hw_04_sol.pdf
hw_05.pdf Gauss-Markov model, estimation, projections, miscellaneous results Thursday, Oct 26th hw_05_sol.pdf
hw_06.pdf Multivariate Normal, distributions of quadratic forms, Cochran's theorem, ANOVA Thursday, Nov 9th hw_06_sol.pdf
hw_07.pdf Likelihood ratio test (F-test), t-test, power, sample size calculations in factorial experiments Tuesday, Nov 28th hw_07_sol.pdf
hw_08.pdf Simultaneous confidence intervals, variance component estimation, mixed models Friday, Dec 8th, by 11:59 pm on Blackboard hw_08_sol.pdf

Exams Solutions
Exam_I.pdf Exam_I_sol.pdf
Exam_II.pdf Exam_II_sol.pdf
Final_Exam.pdf Final_Exam_sol.pdf

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