Linear Statistical Models

Basic Information

Instructor : Siva Athreya .
Teaching Assistant : Ishaan.
Email : athreya@isibang.ac.in
Scoring : 0.1 HW + max(0.6 F + 0.2 max(Quiz1, QUiz2) , 0.4 F + 0.25 QUiz1 + 0.25 Quiz2)
Syllabus: Review of Estimation, Hypothesis Testing, Review of working with R-package Least square estimation. Estimable linear functions. Normal equations. Best Linear Unbiased Estimates (BLUEs). Gauss-Markov Theorem. Fundamental Theorems of Least Square. Testing of linear hypotheses. One-way and two-way classification models: ANOVA and ANCOVA. Nested models. Multiple comparisons Introduction to random effect models.

Texts and References

[W]Applied Linear Regression by Sanford Weisberg
[HG] R for Data Science by Hadley Wickham and Garlett Grolemund.
[VsR] simpleR – Using R for Introductory Statistics by John Verzani (13-15 Section)
[F] Linear Models with R by Julian Faraway

Week #	Notes in Each Week	Homework (Due Dates)	Topics Covered,Recordings, and Code
1	Week-1	(October 8th, 2023) Homework 1 Solutions: Part 1, Part 2	ggplot basics: [HG] Week-1: R-code Recordings: Basic Statistics and Introduction to R https://youtu.be/z1RfnVy8Oak Data Visualization using ggplot2 https://youtu.be/7nmwfGpgDkM Data Visualization using ggplot()-geoms https://youtu.be/EP8uu2k5WfA
2	Week-2	(October 8th, 2023) Homework 2 Solution	Chapter 1 in [W] and Model Basics in [HG] Data Sets: heights.txt, forbes.txt, snow.txt, wblake.txt, turkey.txt Week-2: R-code Recordings: Introduction to Linear Models https://youtu.be/TPJmhTmm4h0 Basics of Linear Models https://youtu.be/Ec94oyf3bKw More on Linear Models - Residuals https://youtu.be/YlAdFp_3j1M Play with more data sets in R https://youtu.be/V8SQrXbSA44
3	Week-3	(October 15th, 2023) Homework 3 Solution	Least square estimation. Estimable linear functions. Recordings: Fundamental of Linear Models and estimation problem https://youtu.be/9RbRhz776-k Theory of linear models https://youtu.be/kAKqc2ftwaA Problem of parameter estimation https://youtu.be/TnJ_1LZXLBk
4	Week-4	(October 22nd, 2023) Homework 4 Solution	Normal equations. Recordings: Different classifications of linear models https://youtu.be/pNIF__GOLGo Normal equations and existence of least square estimates https://youtu.be/Ek-3Ph1AFes Theorem on least square estimates https://youtu.be/XLT3vSQphCg Fundamentals of matrices https://youtu.be/K_j3NHsQ4t8
5	Week-5, Rcode	(October 29th, 2023) Quiz-1	Best Linear Unbiased Estimates (BLUEs). Recordings: Estimating the coefficients of Linear Models https://youtu.be/qF9VBw3CP78 Interval estimate and hypothesis testing for coefficients of Linear Models https://youtu.be/dXYKDrO7vE8 Assess the Linear model by using RSE and R-square https://youtu.be/g1UzPzHITGs Computation of least sqaure estimates in R https://youtu.be/4gwbWg_Gq-4.
6	Week-6	(November 5th, 2023) Homework 6	Gauss-Markov Theorem. Recordings: Introduction to BLUE and Gauss-Markov Theorem https://youtu.be/QPzTQBrHfC4 Proof of Gauss-Markov Theorem https://youtu.be/7L03nVaQgp4 Variance of BLUE and Linear Zero Estimators https://youtu.be/yv-XpOowmwM Assumption of Normality https://youtu.be/TrTyhFMKti8
7	Week-7, R-code	(November 12th, 2023) Homework 7	Fundamental Theorems of Least Squares Recordings: Significance of Gauss Markov Theorem https://youtu.be/9JgEorTBwvw 3D plot of multiple regression in R https://youtu.be/6fNiANvP6tE Linear Regression with real data in R https://youtu.be/lq-HpNWypOg Simulation for sample distribution of least square estimators https://youtu.be/fhYSyDCwhS8
8	Week-8	(November 19th, 2023) Homework 8	Testing of linear hypotheses. Recordings: Introduction to Hypothesis Testing https://youtu.be/aMnMvwu1srA Basic Idea to test simple linear regression https://youtu.be/Zmfc66-MFTQ Testing of linear hypothesis https://youtu.be/UFCYB5jTmyc Proof of second fundamental theorem of least squares https://youtu.be/WV8QQoEG8YA Introduction to ANOVA table https://youtu.be/d8bceej15d0
9	Week-9	(December 11th, 2023) Hw10	One-way and two-way classification models: ANOVA and ANCOVA. Recordings: Testing for one-way classification model https://youtu.be/Jm1OiWqWYj4 Testing of model in general case https://youtu.be/WSs2_OCiajQ Least square estimates of two way classification model https://youtu.be/mKSgszYD93o Testing of two way classification model https://youtu.be/nhxqYZ8X0LA
10	Week-10- R-code	(December 3rd, 2023) Quiz 2	Comparing Means: Testing. Recordings: T-test for SLM in R https://youtu.be/ex_vMbky-MQ T-test for multiple linear regression in R https://youtu.be/hNYZvyRf9qs One way anova in R https://youtu.be/hNiKyEOw2Ig Anova by using basic code in R https://youtu.be/91uaNgCJHQ8
11	Week-11	(December 10th, 2023) Homework 11	Introduction to random effect models. Recordings: Intro to random effect models https://youtu.be/JQP18lxsNtU One way random effect model https://youtu.be/Lhoa2GrnDac Two way random effect model & mixed effect model https://youtu.be/Wz5msD3eca0
12	Week-12,Rcode, Data	(December 17th, 2023) Homework 12	Introduction to random effect models.