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Regression Analysis

Regression Analysis. Instructor: Dr. Soumen Maity, Department of Mathematics, IIT Kharagpur. This course discusses topics in regression analysis: simple linear regression, multiple linear regression, selecting the best regression model, multicollinearity, model adequacy checking, test for influential observations, transformations and weighting to correct model inadequacies, dummy variables, polynomial regression models, generalized linear models, nonlinear estimation, regression models with autocorrelated errors, measurement errors and calibration problem. (from nptel.ac.in)

Course Introduction


Simple Linear Regression
Lecture 01 - Course Introduction, Simple Linear Regression
Lecture 02 - Useful Properties of Least Squares Fit, Statistical Properties of Least Squares Estimators
Lecture 03 - Estimation of σ2, Confidence Intervals and Tests for β0 and β1
Lecture 04 - Analysis of Variance (ANOVA), Coefficient of Determination
Lecture 05 - Confidence Interval of β1, Interval Estimation of the Mean Response, Prediction of New Observation
Multiple Linear Regression
Lecture 06 - Estimation of Model Parameters, Properties of Least Squares Estimators
Lecture 07 - Hypothesis Testing in Multiple Linear Regression
Lecture 08 - Example on Multiple Linear Regression
Lecture 09 - Extra Sum of Squares Method, Confidence Intervals in Multiple Regression
Selecting the Best Regression Model
Lecture 10 - All Possible Regression Approach
Lecture 11 - All Possible Regression Approach (cont.)
Lecture 12 - Sequential Selection: Backward Elimination, Forward Selection
Lecture 13 - Sequential Selection: Forward Selection (cont.), Stepwise Selection
Multicollinearity
Lecture 14 - Multicollinearity
Lecture 15 - Effects of Multicollinearity (cont.), Multicollinearity Diagnostics
Lecture 16 - Multicollinearity Diagnostics (cont.), Methods for Dealing with Multicollinearity
Model Adequacy Checking
Lecture 17 - Residuals: Regular Residuals, Standardized Residuals, Studentized Residuals
Lecture 18 - PRESS Residuals, Residual Plots
Lecture 19 - The Plot of Residual against the Regressor, Partial Residual Plot
Test for Influential Observations
Lecture 20 - Test for Influential Observations
Transformation and Weighting to Correct Model Inadequacies
Lecture 21 - Variance-stabilizing Transformations, Transformations to Linearize the Model
Lecture 22 - Generalized and Weighted Least Square
Lecture 23 - Analytic Models to Select a Transformation
Dummy Variables
Lecture 24 - Dummy Variables to Separate Blocks of Data
Lecture 25 - Interaction Terms Involving Dummy Variables
Lecture 26 - Three Sets of Data and Straight Line Models
Polynomial Regression Models
Lecture 27 - Polynomial Models in One Variable and Orthogonal Polynomials
Lecture 28 - Piecewise Polynomial Fitting
Lecture 29 - Polynomial Models in Two or More Variables
Generalized Linear Models
Lecture 30 - The Exponential Family of Distributions, Fitting Generalized Linear Models
Lecture 31 - Generalized Linear Models (cont.)
Nonlinear Estimation
Lecture 32 - Nonlinear Estimation: Nonlinear Models, Least Square in Nonlinear Case
Regression Models with Autocorrelated Errors
Lecture 33 - Source and Effect of Autocorrelation, Detecting the Presence of Autocorrelation
Lecture 34 - Parameter Estimation in the Presence of Autocorrelation Model
Measurement Errors and Calibration Problem
Lecture 35 - Measurement Errors and Calibration Problem
Tutorials
Lecture 36 - Solving Problems from Simple Linear Regression Model
Lecture 37 - Solving Problems from Linear Regression Models
Lecture 38 - Solving Problems
Lecture 39 - Solving Problems: Coefficient of Determination, Autocorrelated Errors
Lecture 40 - Nonlinear Estimation, Generalized Linear Models, Dummy Variables

References
Regression Analysis
Instructor: Dr. Soumen Maity, Department of Mathematics, IIT Kharagpur. This course discusses topics in regression analysis.