Demo: Data Science Education with WebAssembly

Linear Regression in R and Python

Overview

The goal of this presentation is to showcase the power of WebAssembly (WASM) in data science education by allowing real-time code execution, visualization, and exercises directly within the slide deck.

We do this by exploring the concept of linear regression using both R and Python code snippets.

Introduction

Linear regression is a fundamental statistical technique used to model the relationship between a dependent variable and one or more independent variables.

This presentation will cover:

1. Basic Concepts
2. Implementation in R and Python
3. Model Evaluation
4. Assumptions and Diagnostics

Basic Concepts

Linear regression aims to find the best-fitting straight line through the data points.

The general form of a simple linear regression model is:

\[Y = \beta_0 + \beta_1X + \epsilon\]

Where:

• \(Y\) is the dependent variable
• \(X\) is the independent variable
• \(\beta_0\) is the y-intercept
• \(\beta_1\) is the slope
• \(\epsilon\) is the error term

Generating Data

Let’s look at how to implement linear regression in R and Python by first simulating some data

• R
• Python

Guessing the Coefficients

Try to fit a linear regression model by hand through manipulating coefficients below:

The linear regression with \(\beta_0 =\) and \(\beta_1 =\) is:

import {Tangle} from "@mbostock/tangle"

// Setup Tangle reactive inputs
viewof beta_0 = Inputs.input(0);
viewof beta_1 = Inputs.input(1);
beta_0_Tgl = Inputs.bind(Tangle({min: -30, max: 300, minWidth: "1em", step: 1}), viewof beta_0);
beta_1_Tgl = Inputs.bind(Tangle({min: -5, max: 5, minWidth: "1em", step: 0.25}), viewof beta_1);

// draw plot in R
regression_plot(beta_0, beta_1)

:::

Fit Linear Regression Model

Now that we have our data, let’s fit a linear regression model to it:

• R
• Python

Visualize the Results

We can visualize the data and the regression line to see how well the model fits the data using ggplot2 in R and Matplotlib in Python.

• R
• Python

Predicting New Values

We can use our linear regression model to make predictions on new data:

• R
• Python

Your Turn: Predict New Values!

01:30

Create a new data frame with x values 10, 30, and 60, then use the model to predict the corresponding y values.

• R
• Python

Model Evaluation

We can evaluate the performance of our linear regression model using various metrics:

• R
• Python

Assumptions

Linear regression relies on several assumptions:

1. Linearity
2. Independence
3. Homoscedasticity
4. Normality of residuals

Checking Assumptions with Diagnostics Plots

Let’s look at some diagnostic plots:

• R
• Python

Conclusion

• Linear regression is a powerful tool for modeling relationships between variables.
• Both R and Python offer robust implementations and diagnostic tools.
• Always check assumptions and perform diagnostics to ensure the validity of your model.
• Consider more advanced techniques (e.g., multiple regression, polynomial regression) for complex relationships.