Linear and Logistic Regression

Modelling relationships

Linear regression models a numeric outcome as a linear combination of predictors. In R, lm(outcome ~ predictor1 + predictor2, data = df) fits a model using formula syntax: ~ separates outcome from predictors, + adds terms, * adds interactions, and categorical predictors (factors) are converted to dummy variables automatically. summary() shows coefficients (the expected change in the outcome for a one-unit change in a predictor, holding others fixed), standard errors, p-values and R-squared; confint() gives confidence intervals. Check assumptions with residual plots (plot(model)): roughly linear relationships, constant variance and no influential outliers. Logistic regression models a binary outcome (churned or not, paid or not) with glm(y ~ x, family = binomial, data = df); coefficients are on the log-odds scale, so exp(coef(model)) gives odds ratios. Use predict() for new data (with type = "response" for probabilities). The broom package turns model output into tidy tibbles, and tidymodels provides a consistent framework for preprocessing, resampling and evaluating many model types.

Linear and logistic models

Formulas, summaries, tidy output and predictions.

library(broom)

# linear model: order value explained by number of items and city
fit <- lm(amount_inr ~ items + city, data = sales)
summary(fit)                 # coefficients, R-squared, p-values
confint(fit)
tidy(fit, conf.int = TRUE)   # coefficients as a tibble
glance(fit)                  # model-level statistics
par(mfrow = c(2, 2)); plot(fit)   # residual diagnostics

# logistic model: probability a customer churns
churn_fit <- glm(churned ~ days_since_last_order + orders_last_90d + support_tickets,
                 family = binomial, data = customers)
tidy(churn_fit, exponentiate = TRUE)    # odds ratios

new_customers <- data.frame(days_since_last_order = c(10, 120),
                            orders_last_90d = c(5, 0),
                            support_tickets = c(0, 3))
predict(churn_fit, newdata = new_customers, type = "response")   # churn probabilities

Coefficients are conditional

A coefficient describes the association holding the other predictors fixed, in this data. It is not automatically a causal effect: confounders, selection bias and reverse causation can all produce strong coefficients.

त्वरित जाँच: Which call fits a logistic regression for a binary outcome in R?

• glm(y ~ x, family = binomial)
• lm(y ~ x)
• t.test(y, x)
• cor(y, x)