R Programming - Unit 5

1. Linear regression

• types of linear regression
• R implementation of
  • simple linear regression
  • multiple linear regression

Linear Regression

Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. It aims to find a linear equation that best predicts the dependent variable based on the independent variables.

Types of Linear Regression

1. Simple Linear Regression: Involves one independent variable and one dependent variable. The model is represented as:

   $$Y={\beta }_0+{\beta }_{1}X+ϵ$$

2. Multiple Linear Regression: Involves multiple independent variables. The model is represented as:

   $$Y={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2+\dots +{\beta }_n{X}_n+ϵ$$

R Implementation

# Simple Linear Regression
# Load necessary library
data(mtcars)

# Fit the model
simple_model <- lm(mpg ~ wt, data = mtcars)
summary(simple_model)

# Multiple Linear Regression
# Fit the model with multiple predictors
multiple_model <- lm(mpg ~ wt + hp + qsec, data = mtcars)
summary(multiple_model)

Complexity

• Time Complexity: $O(n^2)$ for the normal equation solution.
• Space Complexity: $O(n)$ for storing data points.

_{This was AI generated from github copilot on 2025-12-23}

2. Plot customization

• Point and click coordinate interaction
• Specialized test and labels
• 3D scatter plot
• Different ways to define colour for plots

R Programming Overview

R is a programming language and environment primarily used for statistical computing and data visualization. It offers a variety of packages and tools to create complex plots and analyze data efficiently.

Basic Plot Customization

You can customize plots using the plot() function. Here is an example of a simple scatter plot with customized labels and colors:

# Simple scatter plot with customization
x <- rnorm(100)  # Generate random normal data for x
y <- rnorm(100)  # Generate random normal data for y

plot(x, y, 
     main = "Customized Scatter Plot", 
     xlab = "X-axis Label", 
     ylab = "Y-axis Label", 
     col = "blue",        # Point color
     pch = 16)           # Point shape

Point and Click Coordinate Interaction

Using the identify() function, you can interactively identify points on a plot:

# Identify points
plot(x, y)
identify(x, y)

Specialized Test and Labels

You can add text labels to specific points using the text() function:

# Add labels to points
plot(x, y)
text(x[1:5], y[1:5], labels = paste("Point", 1:5), pos = 4)

3D Scatter Plot

For 3D plotting, use the plot3D package. Here’s an example:

# 3D Scatter plot
library(plot3D)
x <- rnorm(100)
y <- rnorm(100)
z <- rnorm(100)

scatter3D(x, y, z, col = "red", pch = 19, main = "3D Scatter Plot")

Different Ways to Define Color for Plots

Colors can be defined using names, hexadecimal codes, or RGB values. Here are examples:

# Different color definitions
plot(x, y, col = "green")          # Color name
plot(x, y, col = "#FF5733")        # Hexadecimal
plot(x, y, col = rgb(0.1, 0.5, 0.8)) # RGB values

Mermaid Flowchart Example

A flowchart representing the workflow of plotting in R might look like this:

This overview provides a concise introduction to R programming with a focus on plotting customization and interactivity.

_{This was AI generated from github copilot on 2025-12-23}