Simple Linear Regression Using California Housing Dataset (CSV Input)

 

Experiment 

Simple Linear Regression Using California Housing Dataset (CSV Input)

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Aim

To implement Simple Linear Regression using one feature (total_rooms) from the California Housing dataset (housing.csv) to predict house prices using the top 150 records.

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Objectives

• Load dataset from a CSV file

• Select a single feature and target variable

• Build a regression model manually

• Compute MSE and R² manually

• Visualize regression line

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🛠️ Tools Required

• Python

• NumPy

• Pandas

• Matplotlib

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📖 Theory

🔹 Simple Linear Regression

$$y = b_0 + b_1 x$$

Where:

• $x$: Independent variable (total_rooms)

• $y$: Dependent variable (median_house_value)

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🔹 Regression Coefficients

$$b_1 = \frac{\sum (x - \bar{x})(y - \bar{y})}{\sum (x - \bar{x})^2}$$ $$b_0 = \bar{y} - b_1 \bar{x}$$

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🔹 Mean Squared Error (MSE)

$$MSE = \frac{1}{n} \sum (y_i - \hat{y}_i)^2$$

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🔹 R-squared (R²)

$$R^2 = 1 - \frac{SS_{res}}{SS_{tot}}$$

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📋 Procedure

1. Load dataset from housing.csv

2. Select:

   • Feature: total_rooms

   • Target: median_house_value

3. Use first 150 rows

4. Compute regression coefficients

5. Predict values

6. Compute MSE and R²

7. Plot regression line

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💻 Program

import numpy as np

import pandas as pd

import matplotlib.pyplot as plt

# -----------------------------

# Load dataset

# -----------------------------

df = pd.read_csv("/content/sample_data/housing.csv")

# -----------------------------

# Select feature and target

# -----------------------------

X = df['total_rooms'].head(150).values.reshape(-1, 1)

y = df['median_house_value'].head(150).values.reshape(-1, 1)

# -----------------------------

# Visualization (Scatter Plot)

# -----------------------------

plt.scatter(X, y, color="blue", s=20)

# -----------------------------

# Mean values

# -----------------------------

m_x = np.mean(X)

m_y = np.mean(y)

# -----------------------------

# Compute coefficients

# -----------------------------

SS_xy = np.sum((X - m_x) * (y - m_y))

SS_xx = np.sum((X - m_x) * (X - m_x))

b1 = SS_xy / SS_xx

b0 = m_y - b1 * m_x

print("Slope (b1):", b1)

print("Intercept (b0):", b0)

# -----------------------------

# Predictions

# -----------------------------

y_pred = b0 + b1 * X

# -----------------------------

# Manual MSE

# -----------------------------

n = len(y)

mse = np.sum((y - y_pred) ** 2) / n

print("MSE:", mse)

# -----------------------------

# Manual R²

# -----------------------------

SS_res = np.sum((y - y_pred) ** 2)

SS_tot = np.sum((y - m_y) ** 2)

r2 = 1 - (SS_res / SS_tot)

print("R²:", r2)

# -----------------------------

# Plot regression line

# -----------------------------

plt.plot(X, y_pred, color="red")

plt.xlabel("Total Rooms")

plt.ylabel("Median House Value")

plt.title("Simple Linear Regression (150 Samples)")

plt.show()

 Output

• Scatter plot of data

• Regression line

• Computed values:

• Slope (b₁)

• Intercept (b₀)

• MSE

• R²

Slope (b1): 30.03063864613546 Intercept (b0): 144527.3970744946 MSE: 9070344426.642298 R²: 0.1494586436630212

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Result

The linear regression model was successfully implemented using the total_rooms feature.
Model performance was evaluated using MSE and R².

• The model establishes a linear relationship between total rooms and house price

• Performance depends on how strongly the feature influences the target

• Using only one feature may limit accuracy