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California Housing Dataset Project: Building a Linear Regression Model

Learn to predict housing prices using linear regression with the California Housing Dataset. This guide covers data preprocessing, feature extraction, modeling, and inference for supervised learning.

<h3>California Housing Dataset Project: Building a Linear Regression Model</h3>
In this project, we’ll train a linear regression model to predict median house prices using Google’s California Housing Dataset. This exercise will guide you through data preprocessing, feature extraction, model implementation, and performance evaluation.
<hr>
<h3>Project Overview</h3>
<ol>
<li style="font-size: 14pt;">Dataset: California Housing Dataset, used for regression analysis on house prices.</li>
<li style="font-size: 14pt;">Tools: <code>pandas</code>, <code>numpy</code>, <code>matplotlib</code></li>
<li style="font-size: 14pt;">Goal: Use a linear model to predict housing prices based on various features.</li>
</ol>
<hr>
<h3>Step-by-Step Guide</h3>
<h4>1. Data Loading and Normalization</h4>
<ul>
<li style="font-size: 14pt;">Load the training and testing datasets as pandas DataFrames.</li>
<li style="font-size: 14pt;">Normalize feature values to Z-scores to standardize ranges across features.</li>
</ul>
<h4>2. Data Exploration</h4>
<ul>
<li style="font-size: 14pt;">Explore correlations between features and the target variable, <code>median_house_value</code>, for insights on data relationships.</li>
</ul>
<h4>3. Feature Extraction</h4>
<ul>
<li style="font-size: 14pt;">Extract features and target values into <code>numpy</code> arrays for model training and testing.</li>
</ul>
<hr>
<h3>Modeling and Inference</h3>
<h4>Linear Model Equation</h4>
Implement a linear model:
y^=w⊤x+b\hat{y} = w^\top x + by^=w⊤x+b
where:
<ul>
<li style="font-size: 14pt;">www = weights</li>
<li style="font-size: 14pt;">bbb = bias</li>
</ul>
<h4>Inference and Classification</h4>
For regression, use the above equation directly. For binary classification, apply a sigmoid function:
σ(x)=11+e−x\sigma(x) = \frac{1}{1 + e^{-x}}σ(x)=1+e−x1
<hr>
<h3>Learning: Stochastic Gradient Descent</h3>
Using supervised learning and stochastic gradient descent, adjust weights and bias based on error derivatives to optimize predictions.
<hr>
<h3>Model Evaluation</h3>
Evaluate model performance using Root Mean Squared Error (RMSE) on both the training and test datasets, assessing accuracy and improvements over multiple training loops.

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California Housing Dataset Project: Building a Linear Regression Model

Learn to predict housing prices using linear regression with the California Housing Dataset. This guide covers data preprocessing, feature extraction, modeling, and inference for supervised learning.

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