Introduction to Regression Models

Regression analysis is a statistical technique used to model relationships between variables. It helps predict outcomes and uncover data patterns.

Understanding Linear Regression

Linear regression models the relationship between a dependent and independent variable using a straight line.

model <- lm(mpg ~ hp, data=mtcars)
summary(model)

Visualizing Regression Lines

Use abline() to add a regression line to a scatter plot.

plot(mtcars$hp, mtcars$mpg)
abline(model, col='red')

Multiple Linear Regression

Multiple regression includes more than one independent variable to explain variation in the dependent variable.

model_multi <- lm(mpg ~ hp + wt, data=mtcars)
summary(model_multi)

Checking Model Fit

Use summary() to evaluate regression model quality, including R-squared and p-values.

summary(model_multi)

Performing Logistic Regression

Logistic regression models binary categorical outcomes (e.g., success vs. failure).

data(mtcars)
mtcars$am <- as.factor(mtcars$am)
model_logit <- glm(am ~ hp + wt, data=mtcars, family='binomial')
summary(model_logit)

Predicting New Values

Use predict() to generate predictions from a trained regression model.

predict(model_multi, newdata=data.frame(hp=120, wt=3))

Evaluating Model Assumptions

Regression models assume normality, homoscedasticity, and independence of errors. Check residual plots to assess validity.

plot(model_multi$residuals)

Summary

In this lesson, you learned:

• How to perform linear and multiple regression.
• How to evaluate regression model performance.
• How to predict new values using regression models.