Statistics and linear models

Statistical modelling is what R was built for, and formulas appear across its whole ecosystem.

Descriptive statistics are one call each: mean, median, sd, var, quantile, cor, and table or prop.table for counts. Classical tests are built in: t.test, wilcox.test, chisq.test, cor.test, each returning an object with a p-value and confidence interval.

Models use a formula: y ~ x1 + x2 reads "model y as a function of x1 and x2". Formula operators have special meanings:

x1:x2 is an interaction, x1 * x2 is both main effects plus the interaction.
- 1 removes the intercept; I(x^2) protects arithmetic inside a formula.
Factors are expanded into dummy variables automatically, using the first level as the reference.

fit <- lm(mpg ~ wt + hp, data = mtcars) fits ordinary least squares. Then use generic functions: summary(fit) for coefficients, standard errors and R squared, coef(fit), confint(fit), residuals(fit), predict(fit, newdata) and plot(fit) for diagnostics. anova(fit1, fit2) compares nested models.

glm(y ~ x, family = binomial, data = d) fits logistic regression and other generalised linear models with the same interface. The same formula idea drives aggregate, boxplot, t.test(value ~ group) and many packages, so learning it pays off widely.

Example

fit <- lm(mpg ~ wt + hp, data = mtcars)
print(round(coef(fit), 3))
#> (Intercept)          wt          hp
#>      37.227      -3.878      -0.032
print(round(summary(fit)$r.squared, 3))   #> [1] 0.827

new_cars <- data.frame(wt = c(2.5, 3.5), hp = c(100, 150))
print(round(predict(fit, new_cars), 1))
#>    1    2
#> 24.4 18.9

tt <- t.test(mpg ~ am, data = mtcars)    # automatic vs manual
print(round(tt$p.value, 4))               #> [1] 0.0014

logit <- glm(am ~ wt, family = binomial, data = mtcars)
print(round(predict(logit, data.frame(wt = 3), type = "response"), 2))
#>    1
#> 0.49

Remember

y ~ x1 + x2 formulas describe models; * adds interactions
lm/glm fit, summary/predict/confint inspect
Factors become dummy variables with the first level as reference

Watch out for

Writing y ~ x^2 expecting a square term; inside formulas use I(x^2) or poly(x, 2).

Check yourself

In lm(y ~ a * b), which terms are fitted?

Official docs: cran.r-project.org/doc/manuals/r-release/R-intro.html#Statistical-models-in-R

Example

Remember

Watch out for

Check yourself

Builds on

Unlocks