Regression and its Types in R

Regression analysis is a form of predictive modeling technique that analyzes the relationship between a dependent variable and one or more independent variables. In R, regression models are commonly built using the lm() function for linear regression, but there are various other functions for different types of regressions.

In this tutorial, we'll delve into:

Linear Regression
Multiple Linear Regression
Polynomial Regression
Logistic Regression
Ridge and Lasso Regression

1. Linear Regression

Linear regression aims to model the relationship between a single independent variable and the dependent variable by fitting a linear equation.

# Example
data(cars)
linear_model <- lm(dist ~ speed, data=cars)
summary(linear_model)

2. Multiple Linear Regression

When there's more than one independent variable, you would use multiple linear regression.

# Example using the 'mtcars' dataset
data(mtcars)
multi_linear_model <- lm(mpg ~ wt + hp, data=mtcars)
summary(multi_linear_model)

3. Polynomial Regression

Polynomial regression models the relationship between the independent variable x and the dependent variable y as an nth degree polynomial.

# Quadratic model (2nd degree polynomial)
polynomial_model <- lm(mpg ~ wt + I(wt^2), data=mtcars)
summary(polynomial_model)

4. Logistic Regression

Logistic regression is used when the dependent variable is binary (i.e., 0/1, Yes/No, True/False). It predicts the probability of the dependent event occurring.

# Example using the 'mtcars' dataset, predicting if a car has an automatic transmission
data(mtcars)
mtcars$am <- as.factor(mtcars$am)
logistic_model <- glm(am ~ mpg + hp, data=mtcars, family=binomial)
summary(logistic_model)

5. Ridge and Lasso Regression

These are regularized regression methods, used when multicollinearity exists or when you want to prevent overfitting.

Ridge Regression adds "L2" penalty equivalent to the square of the magnitude of coefficients.
Lasso Regression (Least Absolute Shrinkage and Selection Operator) adds "L1" penalty equivalent to the absolute value of the magnitude of coefficients.

# Using the 'glmnet' package
install.packages("glmnet")
library(glmnet)

# For demonstration purposes, using 'mtcars' dataset
x <- as.matrix(mtcars[, -1]) # excluding the dependent variable
y <- mtcars$mpg

# Ridge regression
ridge_model <- glmnet(x, y, alpha=0)
plot(ridge_model)

# Lasso regression
lasso_model <- glmnet(x, y, alpha=1)
plot(lasso_model)

Conclusion

R provides a wide variety of functions to handle different types of regression models. The choice of regression type depends on the nature of data and the relationship between variables. Each type has its own strengths and weaknesses, so it's important to understand the underlying assumptions and conditions for which each method is appropriate.

R code for simple linear regression:

# Sample data
x <- c(1, 2, 3, 4, 5)
y <- c(2, 3, 4, 4, 5)

# Simple linear regression model
lm_model <- lm(y ~ x)

# Summary of the model
summary(lm_model)

Multiple regression types in R programming: Multiple regression extends linear regression by incorporating multiple independent variables.

# Sample data with multiple predictors
x1 <- c(1, 2, 3, 4, 5)
x2 <- c(2, 3, 4, 5, 6)
y <- c(3, 4, 5, 5, 6)

# Multiple regression model
multiple_lm_model <- lm(y ~ x1 + x2)

# Summary of the model
summary(multiple_lm_model)

Logistic regression in R explained: Logistic regression models the probability of a binary outcome.

# Sample data for logistic regression
x <- c(1, 2, 3, 4, 5)
y <- c(0, 0, 1, 1, 1)

# Logistic regression model
logistic_model <- glm(y ~ x, family = binomial)

# Summary of the model
summary(logistic_model)

Polynomial regression in R examples: Polynomial regression models relationships that are not linear.

# Sample data for polynomial regression
x <- c(1, 2, 3, 4, 5)
y <- c(1, 4, 9, 16, 25)

# Polynomial regression model
poly_model <- lm(y ~ poly(x, degree = 2))

# Summary of the model
summary(poly_model)

Comparing regression types in R: Comparing regression types involves evaluating model fit, performance metrics, and understanding the assumptions of each regression type.
```
# Compare models using AIC
AIC(lm_model, multiple_lm_model, logistic_model, poly_model)
```

Advanced regression techniques in R: Advanced regression techniques include ridge regression, lasso regression, time series regression, and more. These techniques address specific challenges and improve model performance.

# Install and load necessary packages
install.packages(c("glmnet", "forecast"))
library(glmnet)
library(forecast)

# Ridge regression
ridge_model <- glmnet(as.matrix(model_matrix(lm_model)), y, alpha = 0)

# Time series regression
time_series_model <- lm(y ~ time)

# Summary of the models
summary(ridge_model)
summary(time_series_model)