Applied Statistical Modeling for Data Analysis in R

Install and set up R and R Studio, then run scripts for statistical analysis. Knitting R Markdown to HTML creates reproducible analysis records and guides package and directory management.

Explore common R data structures, including vectors, matrices, and data frames, focusing on 1-based indexing, type handling with typeof and as integer, and binding by rows or columns.

Read data into R with read.csv and read.table for csv and txt. Set working directory, preview head, and handle separators and Excel and online data.

Learn to index and subset data frames in R by specifying rows and columns, exploring the Iris dataset with head, str, summary, and subset commands.

Learn to clean data in R by removing missing values with na.omit or complete.cases and imputing with mean, then explore mice imputation and predictive mean mapping.

Explore exploratory data analysis in R using histograms, box plots, and scatter plots to visualize distributions and relationships, illustrated with iris data and ggplot.

Explore measures of center, including mean, median, and mode, and decide when to report the mean or the median using real-world examples and skewness concepts.

Explore how to compute and report variation in data using the mean, standard deviation, standard error, and interquartile range, and visualize it with box plots and five-number summaries.

Visualize continuous data with box plots to compare tooth length across supplements using ggplot, highlighting the five-number summary, outliers, and grouping by factors like race or diet.

Visualize discrete data with bar graphs, using frequency counts and means by group in R. Explore iris, diamonds, and Titanic datasets, and add standard deviation error bars.

Derive insights from qualitative data with chi square tests in R, testing association between gender and food using cross tables and post hoc analysis for n cross n matrices.

Conclude section 3 by summarizing mean and median, variation via standard deviation and interquartile range, and visualizing with boxplots, histograms, and chi-square analysis for categorical associations.

Introduce random variables and distinguish discrete from continuous types. Present discrete distributions (binomial, Poisson, negative binomial) and continuous (normal, t) for statistical modeling in R.

Explore the normal distribution, its bell curve, and how mean, median, and mode coincide. Relate mu and sigma to data spread and the 68-95-99.7% rule for parametric tests in R.

Assess whether data are normally distributed using histograms, qq plots, and the Shapiro-Wilk test in R, with the tooth growth Len variable as an example.

Explore the standard normal distribution, a Z distribution with mean zero and standard deviation one, use the standardization formula to compute Z scores and compare test scores, speeds, and probabilities.

Learn the theory of confidence intervals, including 95% intervals, margin of error, and z vs. t distributions, with practical R calculations.

Learn to compute confidence intervals for the mean in R using z and t values, including standard deviation, standard error, and margin of error, with tooth growth data.

Concludes section four by reviewing discrete and continuous random variables, their distributions, histograms and Shapiro-Wilk checks, Z scores, and confidence intervals in R.

Explore hypothesis testing that uses sample data to test a population claim against the null hypothesis, interpreting p values and alpha levels, power, and avoiding type I and II errors.

Explore t tests as a formal hypothesis-testing tool to compare means, assess significance, and apply one-sided, two-sample, or paired tests using tooth growth and pH examples.

Explore non-parametric alternatives to t tests by comparing medians when data are not normal, using Mann-Whitney and Wilcoxon tests on the CO2 uptake by treatment.

Learn to perform a one-way ANOVA to compare mean weight across three plant growth groups, apply Tukey HSD post-hoc tests, and check homogeneity of variances and normality of residuals.

Explore the non-parametric version of one-way ANOVA using the Kruskal-Wallis test on plant growth weight data, with post-hoc pairwise Wilcoxon tests to identify differences, and preview two-way ANOVA.

Learn to use two-way anova to test how supplement and dose, and their interaction, affect tooth length in tooth growth data, with type iii sums of squares for unequal groups.

Learn to use power tests in R to decide if your sample size can detect meaningful differences with t tests and anovas, using effect sizes, alpha levels, and 80% power.

Apply and interpret one- and two-sided t tests and two-way ANOVA in R, check assumptions, perform post-hoc analyses, and assess test power and required sample size.

Analyze the relationship between two quantitative variables using scatter plots, interpret correlation, and apply regression modeling to distinguish association from causation in data analysis.

Understand correlation, its positive and negative forms, and how to compute and interpret it in R using Pearson, Spearman, and Kendall tau. Learn to visualize and test significance.

Explore the theory of linear regression to model y from predictor variables x, interpret the slope and intercept, and assess fit with ordinary least squares, r-squared, and residuals.

Explore practical linear regression and multiple linear regression in R using iris data, defining y and x with tilde, and interpreting coefficients and adjusted R square for model evaluation.

Assess the four linear regression assumptions: linear relation, normal residuals, independent errors, and homoscedasticity, and avoid multicollinearity, using plots and tests to identify violations and influential points.

Identify multicollinearity by examining correlations among predictors, remove highly correlated variables using a 0.7 cutoff with the caret package, and confirm stability via variance inflation factors in R.

Explore how regression models reveal the relationship between body weight and metabolic rate, interpret the slope and intercept, and assess significance with adjusted R-squared, p-values, and confidence and prediction intervals.

Explore how linear regression and anova relate, using the f test to show the regression model improves prediction over the intercept-only model, with p<0.05 and 75% sepal length variation explained.

Learn to perform linear regression with categorical variables and interaction terms, using dummy variables to model species effects and their interactions, with ANOVA-guided interpretation of intercepts and slopes.

Explore ANCOVA to compare regression lines across rainfall levels while controlling for leaf mass area, test interactions, and compare slopes via confidence intervals.

Learn to build and compare linear regression models using adjusted R square and AIC, select the most parsimonious predictors, address multicollinearity and overfitting, and apply forward, backward, and stepwise selection.

Explore correlation and linear regression, including parametric and nonparametric methods, multicollinearity handling, and interpreting models with r square and anova. Practice forward, backward, and stepwise selection with aic.

Examine how non-normal residuals affect linear regression and apply transforms on iris data, including square root, cube root, log, power law, and box-cox, with back transformation to predict sepal width.

Explore robust and resistant regression techniques when linear regression assumptions fail, using the faithful dataset to predict eruptions from waiting time, and address heteroskedasticity with quantile regression.

Apply standardized major axis regression to data with measurement error, using log transforms to test common slope and scaling factors in allometric relationships.

Explore polynomial and nonlinear regression in R, using linear fits, polynomial terms, orthogonal polynomials, and nonlinear models like Gompertz and Chapman Richards growth models to analyze growth data.

Learn linear mixed effect modeling in R, distinguishing fixed and random effects, and applying random intercepts, random slopes, and time and diet interactions to chicken weight data.

Explore logistic regression in R using GLMs to model binary outcomes with a logit link, interpret coefficients, odds, and probabilities, and assess model fit with deviance and Hosmer-Lemeshow tests.

Explore poisson regression in r for count data using a glm with poisson family and log link, modeling canopy cover as a function of elevation.

Conduct a goodness-of-fit test to decide if Poisson or negative binomial models fit the data, using deviance, residual degrees of freedom, and a chi-square p-value; both show poor fit.

Master regression methods from variable transformations and robust, quantile, and generalized linear models to handle non-normal data, allometric growth, mixed effects, and logistic or Poisson outcomes.

Explore multivariate analysis techniques, including ordination methods such as principal component analysis, correspondence analysis, and nmds, to reveal patterns in species composition across sites with environmental predictors.

Learn unsupervised clustering with k-means to group data by nearest centroids, minimize within-cluster variation, maximize between-cluster separation, and determine cluster count using iris data.

Learn to perform principal component analysis to reduce dimensions, obtain uncorrelated components, and visualize how predictors like sepal and petal measurements explain most data variance.

Learn to build a linear discriminant analysis model that uses a linear combination of sepal and petal measurements to separate iris species, evaluate with LD1 and LD2, SVD, and accuracy.

Explore correspondence analysis, a multivariate technique for categorical data in contingency tables, revealing how species and habitats relate across dimensions that explain most variance.

Explore how to measure similarity and dissimilarity of species composition across boreal forest habitats using Bray-Curtis and Jaccard indices in R's vegan package, with presence-absence conversion and beta diversity analysis.

Visualize similarities and dissimilarities in beetle species across boreal forest habitats with NMDS, an ordination technique. Use transpose data, vegan's metaMDS, and Bray-curtis dissimilarity to compare habitats.

Explore manova to test multiple response variables, such as sepal length and petal length, across iris species using cbind and summary.aov, with multivariate normality considerations.

Explore multivariate analysis concepts and practical tasks, including unsupervised cluster analysis, PCA, dimensionality reduction, LDA, correspondence analysis for categorical data, NMDS, similarity metrics, and multivariate ANOVA.

Explore exploratory data analysis in R with the xda package, producing numb summary statistics for quantitative iris data and care summary for qualitative data, plus scatter plots and box plots.

Read data from online html tables in R with XML and curl, extracting the 2016 Summer Olympics medal table from Wikipedia for further analysis.

Learn to read HTML tables from Wikipedia pages with rvest by using a URL, XPath, and table index to extract table data.

Learn to run R in Google Colab via rpy2, mount drive, and run R code in cells to read CSV data.

Group data by date to compute daily and monthly averages using the time package. Summarize by time across options like day, week, month, and quarter for airport and terminal data.

Posit lets you deploy and share data science projects from your browser, supporting R and Python apps like shiny, streamlit, and dash, with educational pricing and a limited free tier.

Coordinate distributed computing frameworks to split large problems into tasks across nodes, enabling parallel execution, fault tolerance, and scalable data analysis with in-memory processing.

Learn how denoising removes noise from grainy images using wavelet transforms and denoising autoencoders, including deliberate input corruption to train robust neural networks for cleaner results.