R

Run these in RStudio or the R console. x and y are numeric vectors; df is a data frame.

Mean, median

mean(x)
median(x)

Base R has no mode function; names(which.max(table(x))) gives the most frequent value.

Sample SD and variance

sd(x)
var(x)

Both divide by n − 1.

Correlation and covariance

cor(x, y)
cov(x, y)

Combinations

choose(5, 2)

Returns 10.

Binomial

dbinom(2, size = 8, prob = 0.2)
pbinom(2, size = 8, prob = 0.2)

d is exactly 2, p is at most 2.

Poisson

dpois(3, lambda = 3)
ppois(4, lambda = 6)

Normal areas and cutoffs

pnorm(525, mean = 400, sd = 50)
qnorm(0.9, mean = 400, sd = 50)

Critical values

qnorm(0.975)
qt(0.975, df = 15)

CI for a mean from data

t.test(x, conf.level = 0.95)$conf.int

CI for a proportion, textbook formula

p <- 120 / 200
p + c(-1, 1) * qnorm(0.95) * sqrt(p * (1 - p) / 200)

prop.test uses a different method, so its numbers won't match the formula.

Regression

fit <- lm(sales ~ adv, data = df)
summary(fit)

Coefficients, R², t tests, and the F test in one table.

Prediction interval

predict(fit, data.frame(adv = 8), interval = "prediction")

Use interval = "confidence" for the mean response.

VIF

car::vif(fit)

Needs the car package: install.packages("car").