Linear Regression: From Basics to Predictive Modeling

Introduction

Welcome to this fascinating lesson on regression analysis, where we will delve into the realm of Regression. Before we continue working with the California Housing Dataset, we're going to take a brief detour to explain regression with a simpler dataset. This will help us to understand the principles of linear regression, construct a linear regression model in Python, compute coefficients, and predict values with our mathematical model in a more controlled and comprehendible setting. Are you ready to decode regression analysis?

Creating a Simple Dataset

Before implementing our regression model, let's create a simple dataset to be used in our computations. Consider a simple scenario where x represents some feature values (independent variables) and y corresponds to target values (dependent variables). Our aim is to compute the values of y based on x values, therefore finding a line that fits our data. Let's delve into Python code to shape our dataset: Python # We will first define our hypothetical dataset x = [1, 2, 3, 4, 5] # The feature values (independent variable) y = [1, 2, 3, 2, 3] # The target values (dependent variable)

Understanding Regression

y = \beta x + \alpha

Calculation of Regression Line Coefficients

Join the 1M+ learners on CodeSignal

Be a part of our community of 1M+ users who develop and demonstrate their skills on CodeSignal

# Compute the mean (average) of x and y mean_x = sum(x) / len(x) mean_y = sum(y) / len(y) # Calculate the numerator and the denominator for the slope (β) numerator = sum((xi - mean_x) * (yi - mean_y) for xi, yi in zip(x, y)) denominator = sum((xi - mean_x) ** 2 for xi in x) # Compute the coefficients beta = numerator / denominator alpha = mean_y - (beta * mean_x) # Printing Coefficients print('Beta:', beta ,'Alpha:', alpha) # Output: Beta: 0.4 Alpha: 1.0

import matplotlib.pyplot as plt # Visualizing the data plt.scatter(x, y, color='blue') # Actual data points plt.plot(x, y_pred, color='red') # Predicted regression line # Predicting and plotting a single data point x_new = 3.5 # Example new data point y_new_pred = predict_y(alpha, beta, x_new) # Prediction for the new data point plt.scatter(x_new, y_new_pred, color='green', s=100, zorder=5) # Plotting the new predicted point plt.xlabel('X') plt.ylabel('Y') plt.grid(True) plt.show()

Introduction

Creating a Simple Dataset

Understanding Regression

Calculation of Regression Line Coefficients

Join the 1M+ learners on CodeSignal

Implementing the Regression Model

Making Predictions

Visualizing the Data

Lesson Summary and Practice