Appendix C: R Reference - Regression Modeling and Analysis (MATH 4210)

This appendix is a lookup table, not a tutorial. Use it to install R and the course packages once, to find the one-line syntax for reading a course dataset, and to look up any R function you saw in a chapter but forgot how it works. Functions are grouped by the chapter that introduces them; a function used again in a later chapter is not repeated, so if you cannot find something under “your” chapter, check an earlier one.

Installing R for this course¶

The course was built and checked against R 4.6.0. Download it from CRAN for your operating system, then install RStudio Desktop as your editor; it is not required, but it makes running the chapter code much easier.

Every dataset in this book loads with base R alone (read.csv), but several chapters use add-on packages for diagnostics, model selection, and shrinkage. Install all of them once, before you start Chapter 2:

install.packages(c(
  "faraway", "car", "leaps", "lmtest", "ggplot2", "broom",
  "glmnet", "ellipse", "dplyr", "MASS", "boot", "carData", "HistData"
))

MASS and boot ship with R itself, so install.packages will report they are already present; the line above is safe to run regardless. Load a package in any R session with library(packagename) before using its functions; the chapter tables below note which package each function comes from when it is not base R.

Reading course data¶

Every dataset used in this book lives in data/ as a plain CSV, one row per observation, with column headers already set to the names used in the chapters. Read any of them with base R’s read.csv, giving the path relative to the book’s root folder:

toluca <- read.csv("data/toluca.csv")
head(toluca)

  lotsize hours
1      80   399
2      30   121
3      50   221
4      90   376
5      70   361
6      60   224

All chapter R code assumes your working directory is the book’s root folder (the one that contains data/), so every read.csv call in the book uses a path like "data/toluca.csv", never a full file-system path. In RStudio, open the project at the book root, or set it by hand with setwd("path/to/book-myst") before running any chapter’s code. See Appendix E: The Datasets of This Book for the story, provenance, and variable list of every dataset.

How to read the tables below¶

Each row gives the function, the package it comes from (blank means base R, already loaded in any session), a one-line description of what it does, and a minimal example. Functions are listed once, in the chapter where the book first uses them; later chapters build on these without repeating the entry. library(...) itself is not tabulated; load whichever package a function’s row names before calling it.

Chapter 1: Regression as a way of thinking¶

Function	Package	Purpose	Example
`read.csv`	base	Read a CSV file into a data frame.	`d <- read.csv("data/toluca.csv")`
`lm`	base	Fit a linear model by least squares.	`fit <- lm(hours ~ lotsize, data = d)`
`coef`	base	Extract fitted coefficients from a model.	`coef(fit)`
`predict`	base	Compute fitted or predicted values from a model.	`predict(fit)`
`mean`	base	Arithmetic mean of a vector.	`mean(d$hours)`
`min`	base	Smallest value in a vector.	`min(d$lotsize)`
`sum`	base	Sum of a vector’s entries.	`sum(d$hours)`
`nrow`	base	Number of rows in a data frame.	`nrow(d)`
`cor`	base	Pearson correlation between two vectors.	`cor(d$lotsize, d$hours)`
`var`	base	Sample variance of a vector.	`var(d$hours)`
`sapply`	base	Apply a function to each element of a list or vector, simplifying the result.	`sapply(d, class)`
`round`	base	Round a number to a given number of decimal places.	`round(3.14159, 2)`
`plot`	base	Draw a scatterplot or other base-R plot.	`plot(d$lotsize, d$hours)`
`abline`	base	Add a straight line to an existing plot.	`abline(fit)`
`par`	base	Get or set plotting parameters (layout, margins).	`par(mfrow = c(1, 2))`
`data.frame`	base	Build a data frame from named vectors.	`data.frame(x = 1:3, y = 4:6)`

Chapter 2: Simple linear regression¶

Function	Package	Purpose	Example
`residuals`	base	Extract residuals $e_i = Y_i - \hat{Y}_i$ from a fitted model.	`residuals(fit)`
`fitted`	base	Extract fitted values $\hat{Y}_i$ from a fitted model.	`fitted(fit)`
`summary`	base	Print a model’s coefficients, standard errors, $t$ tests, and $R^2$ .	`summary(fit)`
`sqrt`	base	Square root.	`sqrt(25)`
`set.seed`	base	Fix the random-number generator’s starting point for reproducibility.	`set.seed(4210)`
`replicate`	base	Repeat an expression a fixed number of times, collecting the results.	`replicate(1000, mean(rnorm(10)))`
`rnorm`	base	Draw random values from a Normal distribution.	`rnorm(10, mean = 0, sd = 1)`
`sd`	base	Sample standard deviation of a vector.	`sd(d$hours)`

Chapter 3: Inference for simple linear regression¶

Function	Package	Purpose	Example
`confint`	base	Confidence intervals for a model’s coefficients.	`confint(fit, level = 0.95)`
`anova`	base	Analysis-of-variance table for a fitted model.	`anova(fit)`
`qt`	base	Quantile (inverse CDF) of the $t$ distribution.	`qt(0.975, df = 23)`
`qf`	base	Quantile (inverse CDF) of the $F$ distribution.	`qf(0.95, df1 = 1, df2 = 23)`

Chapter 4: Correlation¶

Function	Package	Purpose	Example
`cor.test`	base	Hypothesis test and confidence interval for a correlation.	`cor.test(d$lotsize, d$hours)`
`atanh`	base	Inverse hyperbolic tangent; the Fisher $z$ transform of a correlation.	`atanh(0.86)`
`tanh`	base	Hyperbolic tangent; inverts the Fisher $z$ transform.	`tanh(1.29)`
`qnorm`	base	Quantile (inverse CDF) of the standard Normal distribution.	`qnorm(0.975)`
`aggregate`	base	Compute a summary statistic for each group in a data frame.	`aggregate(hours ~ lotsize, data = d, FUN = mean)`
`which.max`	base	Index of the largest value in a vector.	`which.max(d$hours)`

Chapter 5: Randomization and bootstrap inference for regression¶

Function	Package	Purpose	Example
`sample`	base	Draw a random sample (with or without replacement) from a vector.	`sample(d$hours, size = 25, replace = TRUE)`
`numeric`	base	Create a numeric vector of a given length, filled with zeros.	`numeric(1000)`
`quantile`	base	Sample quantiles of a vector (used for bootstrap percentile intervals).	`quantile(boot_slopes, c(0.025, 0.975))`
`abs`	base	Absolute value.	`abs(-3.5)`
`max`	base	Largest value in a vector.	`max(d$hours)`
`length`	base	Number of elements in a vector.	`length(d$hours)`
`c`	base	Combine values into a vector.	`c(1, 2, 3)`

Chapter 6: Matrix algebra for regression¶

Function	Package	Purpose	Example
`dim`	base	Dimensions (rows, columns) of a matrix or data frame.	`dim(X)`
`head`	base	First few rows of a data frame or matrix.	`head(d)`
`ncol`	base	Number of columns in a matrix or data frame.	`ncol(X)`
`cbind`	base	Bind vectors or matrices together as columns.	`X <- cbind(1, d$lotsize)`
`colnames`	base	Get or set a matrix’s column names.	`colnames(X) <- c("intercept", "lotsize")`
`matrix`	base	Build a matrix from a vector, given its dimensions.	`matrix(1:6, nrow = 2)`
`t`	base	Transpose a matrix.	`t(X)`
`%*%`	base	Matrix multiplication.	`t(X) %*% X`
`isSymmetric`	base	Test whether a matrix equals its own transpose.	`isSymmetric(t(X) %*% X)`
`qr`	base	QR decomposition of a matrix (used internally by `lm`, and for rank checks).	`qr(X)$rank`
`det`	base	Determinant of a square matrix.	`det(t(X) %*% X)`
`solve`	base	Matrix inverse, or solve a linear system $\mathbf{A}\mathbf{x} = \mathbf{b}$ .	`solve(t(X) %*% X)`
`diag`	base	Extract or construct a diagonal matrix.	`diag(3)`
`as.numeric`	base	Coerce an object to a plain numeric vector.	`as.numeric(coef(fit))`
`chol`	base	Cholesky decomposition of a symmetric positive-definite matrix.	`chol(t(X) %*% X)`
`cov`	base	Sample covariance matrix of a data frame or matrix.	`cov(d)`

Chapter 7: The general linear model¶

Function	Package	Purpose	Example
`all.equal`	base	Test near-equality of two numeric objects, up to rounding error.	`all.equal(coef(fit), b_hand)`

Chapter 8: Multiple regression in practice¶

Function	Package	Purpose	Example
`resid`	base	Extract residuals from a fitted model (identical to `residuals`).	`resid(fit)`
`scale`	base	Center and/or scale the columns of a matrix or data frame.	`scale(d[, c("triceps", "thigh")])`
`as.data.frame`	base	Coerce an object (e.g. a matrix) to a data frame.	`as.data.frame(scale(d))`
`deviance`	base	Residual sum of squares of a fitted model.	`deviance(fit)`

Chapter 9: Model diagnostics¶

Function	Package	Purpose	Example
`hatvalues`	base	Leverage values $h_{ii}$ , the diagonal of the hat matrix.	`hatvalues(fit)`
`rstandard`	base	Standardized (internally studentized) residuals.	`rstandard(fit)`
`rstudent`	base	Studentized deleted (externally studentized) residuals.	`rstudent(fit)`
`cooks.distance`	base	Cook’s distance, an overall influence measure for each observation.	`cooks.distance(fit)`
`dffits`	base	DFFITS, the standardized change in a fitted value when one case is deleted.	`dffits(fit)`
`dfbetas`	base	DFBETAS, the standardized change in each coefficient when one case is deleted.	`dfbetas(fit)`
`factor`	base	Convert a variable to a categorical factor.	`d$grp <- factor(d$grp)`
`bptest`	lmtest	Breusch-Pagan test for nonconstant error variance.	`bptest(fit)`
`shapiro.test`	base	Shapiro-Wilk test for Normality of a sample.	`shapiro.test(residuals(fit))`
`dwtest`	lmtest	Durbin-Watson test for autocorrelated residuals.	`dwtest(fit)`
`library`	base	Load an installed package into the current session.	`library(lmtest)`
`sort`	base	Sort a vector in increasing (or decreasing) order.	`sort(cooks.distance(fit))`
`which`	base	Indices of the `TRUE` entries of a logical vector.	`which(hatvalues(fit) > 0.5)`
`range`	base	Minimum and maximum of a vector, as a length-2 vector.	`range(d$hours)`
`tapply`	base	Apply a function to a vector, grouped by a factor.	`tapply(d$hours, d$grp, mean)`
`pf`	base	Cumulative distribution function of the $F$ distribution.	`pf(4.2, df1 = 1, df2 = 23, lower.tail = FALSE)`

Chapter 10: Remedial measures and transformations¶

Function	Package	Purpose	Example
`log`	base	Natural logarithm (base $e$ ).	`log(d$body)`
`boxcox`	MASS	Profile log-likelihood plot for the Box-Cox family of power transformations.	`MASS::boxcox(fit)`
`qchisq`	base	Quantile (inverse CDF) of the chi-squared distribution.	`qchisq(0.95, df = 1)`
`rlm`	MASS	Fit a robust regression by iteratively reweighted least squares, down-weighting outliers.	`MASS::rlm(y ~ x, data = d)`
`rbind`	base	Bind vectors or data frames together as rows.	`rbind(row1, row2)`

Chapter 11: Categorical predictors and interactions¶

Function	Package	Purpose	Example
`relevel`	base	Change which level of a factor is the reference (baseline) level.	`d$rank <- relevel(d$rank, ref = "AsstProf")`
`model.matrix`	base	Build the design matrix $\mathbf{X}$ a model uses, including dummy columns.	`model.matrix(fit)`
`I`	base	Protect an expression from formula notation, so it is used as-is.	`lm(y ~ x + I(x^2), data = d)`
`pmax`	base	Elementwise maximum across two or more vectors.	`pmax(0, x - 5)`
`expand.grid`	base	Build a data frame of every combination of the given values.	`expand.grid(x = 1:3, grp = c("a", "b"))`
`table`	base	Cross-tabulate one or more factors.	`table(d$rank, d$sex)`

Chapter 12: Multicollinearity, variable selection, and validation¶

Function	Package	Purpose	Example
`vif`	car	Variance inflation factors, a multicollinearity diagnostic.	`car::vif(fit)`
`regsubsets`	leaps	Best-subsets search across candidate predictors.	`leaps::regsubsets(y ~ ., data = d)`
`AIC`	base	Akaike information criterion of a fitted model.	`AIC(fit)`
`BIC`	base	Bayesian (Schwarz) information criterion of a fitted model.	`BIC(fit)`
`order`	base	Indices that would sort a vector.	`order(d$hours)`
`formula`	base	Extract or build a model formula object.	`formula(fit)`
`glmnet`	glmnet	Fit a ridge, lasso, or elastic-net penalized regression path.	`glmnet::glmnet(as.matrix(X), y, alpha = 1)`
`cv.glmnet`	glmnet	Cross-validated `glmnet` fit, chooses the penalty by held-out error.	`glmnet::cv.glmnet(as.matrix(X), y, alpha = 1)`
`as.matrix`	base	Coerce a data frame to a plain numeric matrix.	`as.matrix(d[, c("x1", "x2")])`

Chapter 13: Logistic regression¶

Function	Package	Purpose	Example
`glm`	base	Fit a generalized linear model (here, with `family = binomial`).	`glm(damage_bin ~ temp, data = d, family = binomial)`
`confint.default`	base	Wald (asymptotic Normal) confidence intervals for a `glm`’s coefficients.	`confint.default(fit)`
`drop1`	base	Compare a model to each of its one-term-simpler versions (likelihood-ratio tests).	`drop1(fit, test = "Chisq")`
`exp`	base	Exponential function; converts a log-odds coefficient to an odds ratio.	`exp(coef(fit))`
`pchisq`	base	Cumulative distribution function of the chi-squared distribution.	`pchisq(5.2, df = 1, lower.tail = FALSE)`
`outer`	base	Outer product: apply a function to every pair from two vectors.	`outer(1:3, 1:3, "+")`
`cut`	base	Cut a numeric vector into labeled bins (used to build calibration groups).	`cut(fitted(fit), breaks = 5)`

Chapter 14: Poisson regression and the GLM idea¶

Function	Package	Purpose	Example
`poisson`	base	Family object for Poisson `glm` fits (log link by default).	`glm(count ~ x, data = d, family = poisson)`
`quasipoisson`	base	Family object for overdispersed count data; same mean model, inflated variance.	`glm(count ~ x, data = d, family = quasipoisson)`
`gaussian`	base	Family object for `glm` fits with a Normal response (recovers ordinary `lm`).	`glm(y ~ x, data = d, family = gaussian)`
`df.residual`	base	Residual degrees of freedom of a fitted model.	`df.residual(fit)`
`glm.nb`	MASS	Negative-binomial regression, for overdispersed counts.	`MASS::glm.nb(count ~ x, data = d)`

Chapter 15: Regression with time: autocorrelation and forecasting¶

Function	Package	Purpose	Example
`seq_len`	base	Generate the sequence `1, 2, ..., n`.	`seq_len(nrow(d))`
`diff`	base	Lagged differences of a vector.	`diff(d$passengers)`
`subset`	base	Filter rows of a data frame by a logical condition.	`subset(d, year >= 1955)`

Chapter 16: Path analysis and a look ahead¶

No new functions beyond those already tabulated in earlier chapters; Chapter 16 reuses lm, coef, cor, scale, cooks.distance, factor, and relevel to build a path model from a sequence of ordinary regressions.

See Appendix D: Python Reference for the equivalent lookup table in Python, and Appendix E: The Datasets of This Book for full documentation of every dataset named in the examples above.