STAT 425 - Fall 2024 - Sections 1 and 2
STAT 425 - Fall 2024 - Sections 1 and 2
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From Douglas Simpson
92 plays 0Considers 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… -
From Douglas Simpson
68 plays 0Discusses how blocking is used in experimental design, and how the design affects how we analyze the data. In randomized complete blocks designs, the treatment… -
From Douglas Simpson
48 plays 0Discusses the difference between observational studies and experimental studies. Introduces key ideas and examples of experimental design including randomization,… -
From Douglas Simpson
149 plays 0Discusses 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… -
From Douglas Simpson
228 plays 0Extends 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… -
From Douglas Simpson
245 plays 0Suppose 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… -
From Douglas Simpson
333 plays 0A 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… -
From Douglas Simpson
226 plays 0Examples and computational details for Lasso regression, i.e., L1 penalized least squares. -
From Douglas Simpson
201 plays 0Examples and computational details for principal component regression. -
From Douglas Simpson
225 plays 0Introduces penalized least squares methodology for stabilizing linear regression with correlated or high dimensional predictors. Two key methods are Ridge Regression,… -
From Douglas Simpson
281 plays 0Discusses principal component regression as a way to both understand the variation in the regression predictor variables, and potentially reduce the dimension of the… -
From Douglas Simpson
234 plays 0We walk through R code for variable selection in multiple linear regression, focusing on analysis of state level data relating average life expectancy with key… -
From Douglas Simpson
281 plays 0In selecting predictor variables to include in a regression model, an important consideration is the bias-variance tradeoff: adding variables to the model generally… -
From Douglas Simpson
347 plays 0Analysis of covariance (Ancova) models include both numerical and categorical predictor variables. We discuss building and interpreting Ancova models, emphasizing the… -
From Douglas Simpson
248 plays 0Includes computational details for B-spline and natural cubic spline curve fitting. Also demonstrates how to perform cross-validation for selecting the optimal number… -
From Douglas Simpson
328 plays 0Regression 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… -
From Douglas Simpson
351 plays 0Often 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… -
From Douglas Simpson
306 plays 0Provides 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… -
From Douglas Simpson
299 plays 0Considers 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… -
From Douglas Simpson
349 plays 0If 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… -
From Douglas Simpson
198 plays 0Demonstrates 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… -
From Douglas Simpson
292 plays 0Collinearity between explanatory variables can make it difficult to interpret the individual effects of variables in the model. Building on the added variable / partial… -
From Douglas Simpson
427 plays 0Methods for detecting and characterizing unusual observations in the data relative to the regression model. Unusual observations include: 1) high leverage observations;… -
From Douglas Simpson
312 plays 0R Markdown presentation of several examples for graphical and formal statistical evaluations of modeling assumptions. Provides additional details for several examples in… -
From Douglas Simpson
382 plays 0Discusses how to check for violations of the Gauss-Markov modeling assumptions of constant variance, uncorrelated errors and linearity of the mean function. We consider… -
From Douglas Simpson
360 plays 0Demonstrate coding and interpretation of diagnostic regression plots and statistics for several data examples. Includes pairwise scatter plots, standardized and… -
From Douglas Simpson
377 plays 0Demonstrates coding of Anova F tests, permutation F tests, confidence intervals, prediction intervals and the construction of elliptical confidence regions for two… -
From Douglas Simpson
335 plays 0This video discusses both individual and simultaneous confidence intervals and regions for linear regression coefficients, along with model-based confidence intervals… -
From Douglas Simpson
413 plays 0This video covers hypothesis testing for coefficients in the linear model, based on Gaussian error assumptions. We use coefficient t-tests for individual explanatory… -
From Douglas Simpson
477 plays 0This video shows how to derive the expectation vector, covariance matrix and joint distribution for LS estimators in multiple linear regression. Using the same general…