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Multiple Linear Regression: Partitioning the Residual Sum of Squares
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Classroom Contents
General Linear Models - Regression
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- 1 Introduction to Linear Models
- 2 Simple Linear Regression
- 3 Simple Linear Regression: Properties of Least Squares Estimators
- 4 Simple Linear Regression: Estimating the Residual Variance
- 5 Simple Linear regression: Matrix Notation
- 6 Simple Linear Regression: Maximum Likelihood Estimation
- 7 Simple Linear Regression: Partitioning Total Variability
- 8 Simple Linear Regression: Matrix Notation for Sum of Squares
- 9 Simple Linear Regression: ANOVA Table
- 10 Simple Linear Regression: Testing the Model is Useful
- 11 Simple Linear Regression: LSEs are Normally Distributed
- 12 Simple Linear Regression: Confidence intervals for Beta Parameters
- 13 Simple Linear Regression: Coefficient of Determination
- 14 Simple Linear Regression:Confidence and Prediction Intervals on the Mean and Individual Response
- 15 Simple Linear Regression: Simultaneous Inference on B0 and B1
- 16 Simple Linear Regression: Bonferroni and Working-Hotelling Adjustments
- 17 Simple Linear Regression: Residuals and their Properties
- 18 Simple Linear Regression: X and Y Random
- 19 Simple Linear Regression: Test for the Correlation Coefficient
- 20 Simple Linear Regression: Fixed Zero Intercept Model
- 21 Multiple Linear Regression: Introduction
- 22 Multiple Linear Regression: Least Squares Estimates
- 23 Multiple Linear Regression: The Hat Matrix
- 24 Multiple Linear Regression: Estimating the Error Variance
- 25 Multiple Linear Regression: Projection and Idempotent Matrices
- 26 Multiple Linear Regression: Gauss Markov Theorem
- 27 Multiple Linear Regression: Partitioning Total Variability
- 28 Multiple Linear Regression: Type I Sum of Squares
- 29 Multiple Linear Regression: Type II Sum of Squares
- 30 Multiple Linear Regression: Global F Test
- 31 Multiple Linear Regression: Partial F Tests
- 32 Multiple Linear Regression: t Tests for a Single Beta Parameter
- 33 Multiple Linear Regression: General Linear Hypotheses
- 34 Using R: Simple Linear Regression from Scratch
- 35 Multiple Linear Regression: CI/PI on the Mean and Individual Response
- 36 Multiple Linear Regression: Simultaneous Inference of B'=(B0,B1, ... ,Bk)
- 37 Multiple Linear Regression: Partitioning the Residual Sum of Squares
- 38 Multiple Linear Regression: Repeated Observations and Lack of Fit Test
- 39 Multiple Linear Regression: Centering and Scaling the Design Matrix
- 40 Multiple Linear Regression: Condition Number / Multicollinearity
- 41 Multiple Linear Regression: Variance Inflation Factor (VIF) / Multicollinearity
- 42 Multiple Linear Regression: Variance Proportions / Multicollinearity
- 43 Multiple Linear Regression: Indicator / Dummy Variables
- 44 Multiple Linear Regression: AIC (Akaike Information Criterion)
- 45 Multiple Linear Regression: Choosing a model with R2, Adjusted R2, and MSE
- 46 Multiple Linear Regression: Mallow's Cp
- 47 Multiple Linear Regression: Impact of Under or Over Fitting a Model
- 48 Multiple Linear Regression: The PRESS Prediction SS Statistic
- 49 Multiple Linear Regression: Residual Properties
- 50 Weighted Least Squares Regression: Mahalanobis Distance
- 51 Weighted Least Squares Regression: Hat Matrix
- 52 Weighted Least Squares Regression: Estimability / BLUE
- 53 Weighted Least Squares Regression: Estimating the Error Variance
- 54 Weighted Least Squares Regression: Testing for Estimable Functions
- 55 Weighted Least Squares Regression: Partial F Tests
- 56 Multiple Linear Regression: Canonical Form
- 57 Multiple Linear Regression: Canonical Form and Multicollinearity
- 58 Multiple Linear Regression: Principal Components Model
- 59 Ridge Regression (part 1 of 4): Variance Reduction
- 60 Ridge Regression (part 2 of 4): Deriving the Bias
- 61 Ridge Regression (part 3 of 4): Deriving from 1st principles.
- 62 Ridge Regression (part 4 of 4): Canonical Form
- 63 Multiple Linear Regression: Box-Cox Transformation
- 64 Multiple Linear Regression: Box - Tidwell Transformation
- 65 Multiple Linear Regression: Studentized Residuals (Part 1 of 2)
- 66 Multiple Linear Regression: Studentized Residuals (Part 2 of 2)
- 67 Multiple Linear Regression: Partial Regression Plots (Added Variable Plots)
- 68 Multiple Linear Regression: Influence Measures (Part 1 of 2)
- 69 Multiple Linear Regression: Influence Measures (Part 2 of 2)
- 70 Best quadratic unbiased estimator of variance in a MLR model using Lagrange Multipliers
