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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)

Lecture 37 - Solving Problems from Linear Regression Models

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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