Linear models with lm

lm() is R's built-in function for linear regression. The output is rich with information — coefficients, standard errors, R-squared, F-test, residual diagnostics — and the broom package wraps it into tidy data frames you can pipe into more dplyr.

Fitting an OLS regression

model <- lm(lending_rate ~ deposit_rate, data = bankrates)
summary(model)

The formula syntax y ~ x is the heart of R's modelling interface. lm parses the formula, builds the design matrix, fits OLS, and returns an lm object.

Multiple predictors

model <- lm(lending_rate ~ deposit_rate + month, data = bankrates)

# Interactions: * means main effects + interaction; : means interaction only
lm(y ~ x * z, data = df)   # x + z + x:z
lm(y ~ x:z, data = df)      # x:z only

Reading summary(model)

• Coefficients: estimate, std error, t value, Pr(>|t|)
• Residual standard error: sqrt of mean squared residual
• Multiple R-squared: fraction of variance explained
• F-statistic: joint test of all coefficients = 0
• Stars: significance codes — informally read but technically a p-hacking warning sign in published work

broom — tidying regression output

library(broom)

tidy(model)        # data frame: term, estimate, std.error, statistic, p.value
glance(model)      # one-row data frame: r.squared, adj.r.squared, p.value, etc.
augment(model)     # original data + fitted values + residuals

Predict and confidence intervals

predict(model, newdata = data.frame(deposit_rate = 0.06))
predict(model, interval = "confidence")
predict(model, interval = "prediction")  # wider — for new observations