STAT 425 - Fall 2024 - Sections 1 and 2
STAT 425 - Fall 2024 - Sections 1 and 2
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Considers the extension of ANOVA models to include factors that are themselves random variables. This type of modeling is useful to account for batch correlations in the…
STAT 425 Week 14 - Linear Models with Random…
From Douglas Simpson
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Discusses how blocking is used in experimental design, and how the design affects how we analyze the data. In randomized complete blocks designs, the treatment…
STAT 425 Week 14 - Experimental Design - Part 2
From Douglas Simpson
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Discusses the difference between observational studies and experimental studies. Introduces key ideas and examples of experimental design including randomization,…
STAT 425 Week 13 - Experimental Design - Part 1
From Douglas Simpson
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Discusses analysis and interpretation of results for unbalanced two-way designs. In this case we rely on the general linear model formulation and test each effect after…
STAT 425 Week 12 - Two-Way Anova Models - Part 2:…
From Douglas Simpson
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Extends the analysis of variance to models with two or more factor variables. By doing two-way and multiway analysis of the factor effects we can determine whether there…
STAT 425 Week 12 - Two-Way Anova Models - Part…
From Douglas Simpson
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Suppose we detect differences between the group means in the analysis of variance. We would like to know how those means differ. Characterizing the mean differences…
STAT 425 Week 11 - Analysis of Factor Level Means
From Douglas Simpson
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A one-way anova design is a comparative study in which we compare responses between several treatments, groups or factor levels. Often the subjects or experimental units…
STAT 425 Week 11 - One-way Anova Designs
From Douglas Simpson
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Examples and computational details for Lasso regression, i.e., L1 penalized least squares.
STAT 425 Week 10 - R Examples for Shrinkage -…
From Douglas Simpson
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Examples and computational details for principal component regression.
STAT 425 Week 10 - R Examples for Shrinkage -…
From Douglas Simpson
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Introduces penalized least squares methodology for stabilizing linear regression with correlated or high dimensional predictors. Two key methods are Ridge Regression,…
STAT 425 Week 10 - Shrinkage Methods for…
From Douglas Simpson
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Discusses principal component regression as a way to both understand the variation in the regression predictor variables, and potentially reduce the dimension of the…
STAT 425 Week 10 - Shrinkage Methods for…
From Douglas Simpson
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We walk through R code for variable selection in multiple linear regression, focusing on analysis of state level data relating average life expectancy with key…
STAT 425 Week 09 - R Examples for Variable…
From Douglas Simpson
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In selecting predictor variables to include in a regression model, an important consideration is the bias-variance tradeoff: adding variables to the model generally…
STAT 425 Week 09 - Variable Selection
From Douglas Simpson
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Analysis of covariance (Ancova) models include both numerical and categorical predictor variables. We discuss building and interpreting Ancova models, emphasizing the…
STAT 425 Week 09 - Analysis of Covariance…
From Douglas Simpson
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STAT 425 Week 09 - R Examples for Regression… 15 of 30
STAT 425 Week 09 - R Examples for Regression…
Includes computational details for B-spline and natural cubic spline curve fitting. Also demonstrates how to perform cross-validation for selecting the optimal number…STAT 425 Week 09 - R Examples for Regression…
From Douglas Simpson
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Regression splines provide a flexible family of curves that can be fit to data using ordinary least squares linear model methods, yet closely model arbitrary smooth…
STAT 425 Week 08 - Regression Splines
From Douglas Simpson
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Often the expected response is nonlinear as a function of a predictor variable. These notes show how we can fit polynomial curves to such nonlinear response data while…
STAT 425 Week 08 - Polynomial Regression
From Douglas Simpson
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Provides computing details for examples of generalized least squares regression and lack of fit testing. The coding of factor variables for the lack of fit test is…
STAT 425 Week 08 - R Examples for GLS and Lack of…
From Douglas Simpson
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Considers how to test whether the systematic part of a linear model fits the data. The key idea is to compare the model-based estimate of the error variance to either…
STAT 425 Week 07 - Testing for Lack of Fit
From Douglas Simpson
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STAT 425 Week 06 - Generalized Least Squares… 20 of 30
STAT 425 Week 06 - Generalized Least Squares…
If the errors in the linear model are heteroscedastic or correlated with known structure, or in ways that can be modeled, generalized least squares (GLS) estimation can…STAT 425 Week 06 - Generalized Least Squares…
From Douglas Simpson
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Demonstrates the computational details for collinearity diagnostics in analysis of the car seat position data, and shows how the model can be improved by selecting a…
STAT 425 Week 06 - R Examples for Collinearity
From Douglas Simpson
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Collinearity between explanatory variables can make it difficult to interpret the individual effects of variables in the model. Building on the added variable / partial…
STAT 425 Week 06 - Collinearity
From Douglas Simpson
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Methods for detecting and characterizing unusual observations in the data relative to the regression model. Unusual observations include: 1) high leverage observations;…
STAT 425 Week 04 - Regression Diagnostics - Part…
From Douglas Simpson
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STAT 425 Week 05 - R Examples for Regression… 24 of 30
STAT 425 Week 05 - R Examples for Regression…
R Markdown presentation of several examples for graphical and formal statistical evaluations of modeling assumptions. Provides additional details for several examples in…STAT 425 Week 05 - R Examples for Regression…
From Douglas Simpson
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Discusses how to check for violations of the Gauss-Markov modeling assumptions of constant variance, uncorrelated errors and linearity of the mean function. We consider…
STAT 425 Week 05 - Regression Diagnostics - Part 2
From Douglas Simpson
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STAT 425 Week 05 - R Examples for Regression… 26 of 30
STAT 425 Week 05 - R Examples for Regression…
Demonstrate coding and interpretation of diagnostic regression plots and statistics for several data examples. Includes pairwise scatter plots, standardized and…STAT 425 Week 05 - R Examples for Regression…
From Douglas Simpson
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Demonstrates coding of Anova F tests, permutation F tests, confidence intervals, prediction intervals and the construction of elliptical confidence regions for two…
STAT 425 Week 04 - R Computations for Analysis of…
From Douglas Simpson
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This video discusses both individual and simultaneous confidence intervals and regions for linear regression coefficients, along with model-based confidence intervals…
STAT 425 Week 04 - Multiple Linear Regression -…
From Douglas Simpson
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This video covers hypothesis testing for coefficients in the linear model, based on Gaussian error assumptions. We use coefficient t-tests for individual explanatory…
STAT 425 Week 03 - Multiple Linear Regression -…
From Douglas Simpson
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This video shows how to derive the expectation vector, covariance matrix and joint distribution for LS estimators in multiple linear regression. Using the same general…
STAT 425 Week 03 - Multiple Linear Regression -…
From Douglas Simpson
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