This sheet deals specifically with formulas for linear models and related bivariate analyses. Material related to categorical data will be published elsewhere.

Control Chart Factors, also known as control chart constants, are critical components used in the creation and interpretation of control charts in statistical process control (SPC). These factors help in calculating control limits and other chart parameters, ensuring that the process variability is accurately monitored.

The prop.test function in R is used to perform a test of proportions. It allows you to test whether the proportions in one or more groups are equal to specified values or whether the proportions in two or more groups are equal. This function is often used in hypothesis testing to compare proportions in different samples.

Critical Values for Chi Square Test

The Dixon Q Test, also known simply as the Q Test, is a statistical test used to identify and reject outliers in a small data set. It's particularly useful for normally distributed data sets with fewer than 30 observations.

Combining R graphics into a single composite plot.

Statistical Modelling with R - Introduction to Survival Models

Survival Analysis - Cox Regression Modelling

Introduction to Probability Distributions - Worked Examples of the Normal Distribution

Introduction to Probability - The Poisson Distribution

ETL and Data Pipelines - Coursera Data Engineering Specialization

Data Warehousing and BI Analytics

Chi Square Test for Independence

Vectors and Vector Operations

The Binomial Distribution

The Exponential Distribution

Introduction to Statistics and Probability - The Normal Distribution

The Geometric Distribution

Linux Course Notes

Bivariate Data Analysis

The {MASS} R Package

Modelling Count Variables with R

Statistical Methods for Forestry

Introduction to tidymodels - draft of a workshop on tidymodels

Draft Material for a Workshop on Working with Databases for R Users

Draft Material for a presentation on {duckdb} for R Users

The {brms} R package

Material for a talk on the use of R in commercial forestry

Worked example of ggdist

draft material for an introductory workshop on GIS with R in 2025

Draft material for introductory workshop on Docker for R Users

The Systolic Blood Pressure data, which is commonly used as an exemplar dataset in the clinical analysis of measurement dat. The key feature of this dataset is the simultaneous measurement by three devices on the set of patients.

The reactable package in R allows you to create interactive data tables. It’s a powerful tool for building customizable tables in web applications and R Shiny dashboards. You can use the reactable() function to create tables from data frame

Draft on a talk for the tidypolars R package

Introduction to Logistic Regression and Implementation of logistic regression models with R

The Importance of Repeatability in Method Comparison Studies, and the Coefficient of Repeatability

Adjacent Analyses to Method Comparison Studies

Creating a Bland-Altman Plot from First Principles with R

Introduction to Time Series with R

Regression of Pairwise Differences and Sums

Proposal of an addition of an ellipse to the Bland-Altman plot

Enhancement of Bland-Altman Plots proposed by Bland-Altman 1986

"Statistical methods for assessing agreement between two methods of clinical measurement. (Lancet 327, 307–310 (1986)" by Bland, J. M. & Altman, D. G. is one of the most cited papers of all time. This analysis tracks the citation history by since the paper's publication in the Lancet in 1986.

Technology Acceptance Model

Working with Numbers and Integers

Matthews Correlation Coefficient

Assessing Model Fits with Cook's Distance

Discussion about Deviance Residuals in GLMs

Air Quality Measurements

The Air Passengers Dataset

Kaplan Meier Survival Models

In a study of cheddar cheese from the LaTrobe Valley of Victoria, Australia, samples of cheese were analyzed for their chemical composition and were subjected to taste tests. Overall taste scores were obtained by combining the scores from several tasters.

Graphical Methods for Method Comparison

Introduction to K-Means Clustering with R

The rleid() function in the {data.table} R package

Demonstration of Interval Regression using a worked example involving education data

Multinomial Logistic Regression

Model Validation for Principal Component Analysis

Choosing the Number of PCA Components

Fitting Variance-Covaiance matrices to LME models

Processing categorical data (factors) with the {forcats} R package

Deomstration of the {olsrr} R package

Demonstration of PCA on the Wine Dataset

One Hot Encoding

Demonstration of Mean Imputation for Missing Values using a worked example with R

Extensions of the conventional OLS linear models

Using the Akaike Information Criterion (AIC) for appraising linear model

Definitions of R-Square Measures for Model Appraisal for Linear Models

Demonstration of Huber Weighting for Robust Regression

Testing the assumption of a normal disttributed data set.

Testing Normality in data to validate the required assumptions for inference procedures

Quasi-Poisson Regression

Implementation of ceres plots for model diagnostics using the ceresPlots() function in the {car} R pacakge

Introduction to Robust Regression

Examining various Psi Operators for Robust Regression using the stackloss data set

Introduction to Truncated Regression

Introduction to Tobit Regression

inspectdf is collection of utilities for columnwise summary, comparison and visualisation of data frames.

modelr is a package that helps you create elegant pipelines when modelling with the pipe operator in R. It provides functions for partitioning, resampling, model quality metrics, and interactions with models.

Nonlinearity in Linear Models

Influence Measures for Linear Models

Assumptions for Linear Models

Tests for Collinearity In Regression Models

Non Parametric Statistical Procedures with R

Using R to analyse the Monty Hall Problem

Zero-Inflated Poisson Regression

Implementation of Cohen's Kappa using the {vcd} R package

The {gvlma} package is a comprehensive, automatic testing suite for many of the assumptions of general linear models. It does both statistical tests and diagnostic plots using an extremely simple implementation for powerful results.

Demonstration of the {car} R package using the Prestige dataset as an example

The {broom} R package

Bartlett's test for Homogeneity of Variances

<Draft> Log Transformation of Data

Introduction to the main set of Inference Procedures used in R

Influence Measures for LME Models

Key definitions for Model Diagnostics

Storms and other severe weather events regularly cause public health disasters and economic hardships. These events often result in fatalities, injuries, and property damage. This analysis is a brief exploration of the U.S. National Oceanic and Atmospheric Administration's (NOAA) storm database. This database tracks when and where events occur along with estimated impacts.

Adding smoothed regression lines to ggplot scatterplots

Coursera Data Science Specialization - Quiz 4 for Regression Module

ggplot2 visualizations with the Diamonds Data set

Implementing Ordinal Logistic Regression on the Student College Applications data set using the {polr} command from the {MASS} R package

Implementation of the Binomial Test with R

In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than two possible discrete outcomes.

Analysis of Correlation of two numeric variables with R

Using R to test the association of two categorical variables

Using the Bartlett Test and Fligner Test to test the assumption of homogeneity of variances, as part of an overall ANOVA procedure.

Quiz 1 for the Regression module as part of Coursera's Data Science Specialization

"gglikert()" generate a ggplot2 plot for a Likert 5-scale question

Demonstration of Negative Binomial Regression using the "Days Absent" data set

Logistic Regression with the Pima Diabetes Dataset

Visualizations for the CEL data set

Visualizations for the mpg data set in ggplot2

using "repeat" for iteration. The loop is broken with a break statement triggered by a logical condition

Demonstration of LME model fitting for the Machines Data Set using the {nlme} R package

An exploration of the Orthodont data set, using models fitted by the {nlme} R package

Demonstration of Benfords Distribution using {VGAM}

Outlier Detection with Mahalanobis Distances

Using R and the {Renext} R pacakge to work with the Lomax Distribution (also known as the Pareto Type 2 Distribution)

Probability Distributions with R - The Weibull Distribution

System Date and Time

Implementation of the Kolmogorov-Smirnov Test using R

Implementation of the Wilcoxon Test using R

Implementation of the Friedman Test using the Warpbreaks data set

Exercise for the Visualizing Data in the Tidyverse module - as part of the Coursera Tidyverse Specialization

Making Cluster plots with "geom_encircle()" from the {ggalt} R pacakge

Plotting time series data with the {highcharter} R package

Using the ggpairs() and ggscatmat() functions from the {GGally} R package to visualize bivariate data

The Conover-Iman test is a post hoc test that perform pairwise comparisons using the same rankings used in the Kruskal-Wallis test

How to perform the Kruskal Wallis Test in R

Making Silhouette plots with the {DataVisualization} R package

Comparison of Weighting Methods for Robust Regression using R.

Making roseplots with {ggplot2}

Demonstration on how to create Correlation Plots using the ggcorrplot R package.

making treemaps with the treemapify R package

The Mahalanobis distance is the distance between a data point and the origin (mean) in a multivariate space, and is often used to identify outliers in multivariate statistical analyses.

Mosaic plot with information about missing/imputed values

Using R to make waterfall plots

Demonstration on making interactive Sankey plots with R and networkD3.This post is an amalgam of various gists and solutions on Stack Exchange.

The output is interactive and can not be run in R markdown

A demonstration on how to use R for an exercise from a Royal Statistical Society examination paper (Module 3 2011 Question 3)

A demonstration on how to use R for an exercise from a Royal Statistical Society examination paper (Module 3 2011 Question 1)

An alternative to nested loops using the "cross2()" function trom the {purrr} pacakge

Statistical Analysis of Toothgrowth data set. This is the second part of project work for the Statistical Inference module for Coursera's Data Science Specialization

Truncated regression is used to model dependent variables for which some of the observations are not included in the analysis because of the value of the dependent variable.

Resampling with tidymodels

Using {tidymodels} with the NYCflights13 data

The R package {influence.ME} allows you to compute measures of influential data for mixed effects models generated by {lme4}.

Growth in followership of variousR User Community language company pages on LinkedIn

Growth in followership of various Data Science language company pages on LinkedIn

Growth in followership of various Julia programming language company pages on LinkedIn

Worked Example of a CS2B R programming actuarial exam question, featuring Survival Analysis

Homework exercise for the "Wrangling Data in the Tidyverse Project" module in the Tidyverse Skills for Data Science in R Specialization

Homework exercise for the "Importing Data into R Project" module in the Tidyverse Skills for Data Science in R Specialization

Worked Example of a CS1B R programming actuarial exam question, featuring the Exponential Distribution

In statistics, leverage is a term used in connection with regression analysis and, in particular, in analyses aimed at identifying those observations that are far away from corresponding average predictor values.

A look at Cook's Distance for appraising and identifying influential observation in linear models in R.

Demonstration on how to create a dataframe that comprises differences between two snapshot data frames, i.e. dataframes of identical construction, but containing information at different timepoints

Worked Example of a CS2B R programming actuarial exam question, featuring simulated Claim values

Worked Example of a CS2B R programming actuarial exam question, featuring Mortality Investigation Analysis

Worked Example of a CS2B R programming actuarial exam question, featuring K-Means Cluster Analysis

Worked Example of a CS2B R programming actuarial exam question, featuring Cox Regression

An examination of the Dispersion Parameter, which informs on which approach to use when modelling count variables.

Poisson Regression example using the crabs data set (from the {glm2} R pacakge. This data set is derived from Agresti (2007, Table 3.2, pp.76-77). It gives 4 variables for each of 173 female horseshoe crabs.

Worked Example of a CS2B R programming actuarial exam question, featuring the simulation of a compound probability distribution

Worked Example from the CS2B R programming actuarial examination. This is a time series analysis example using the Air Passengers data set.

Worked example of CS2B R programming actuarial exam question

Worked Example of an exercise on a CS1B R programming exam paper

Using DFFITS, DFBETA and PRESS to determine influential observations in a fitted linear model

Demonstration of how to perform the test for homoscedasticity of residuals of a linear model using the {car} R package

Demonstration of how to perform the Durbin-Watson test for a linear model using the {car} R package

Demonstration of Patchwork R package. This is course material for the "Visualizing Data in the Tidyverse" which is part of the "Tidyverse Skills for Data Science in R Specialization"

Demonstration of how to create simple model diagnostic plots using in-built function in R

Demonstration of Tobit Regression

Demonstration of the functions offered by the car R package for model diagnostics. Here the R package is used to assess linear models fitted on the prestige dataset.

Various options for sequence indices for data frames

Working with a subset of a United States medical expenditures dataset with information on costs for different medical conditions and in different areas of the country.

Using the "var.test()" function in R to assess the validity of statistical assumptions in inference procedures

Demonstration of the intuition of Variance and Standard Deviation as measures of dispersion in statistics

Implementation of the Grubbs' Test for Outliers in a univariate data set using R.

Using logistic regression to predict university admission.

Using {ggplot2} to assess the distributions of univariate data, comparing across categories

Demonstration of ggmosaic R package for visualizing categorical data

A demonstration of Deming Regression, an interesting alternative to OLS regression models that has applications in Method Comparison Studies

This approach require a bespoke function that transforms a dataframe into a suitable hierarchical data structure

Cousera's Data Science Specialization

Data Visualization in R with ggplot2 - Assignment 1

Draft One

Draft 1