Assignment no. 4. Practical Assignments on Statistical / Algorithmic Data Modeling

Objective:

To develop skills in statistical data modeling, hypothesis testing, classification and regression

algorithms, model evaluation techniques, and hands-on exercises with the scikit-learn library.

4.2: Basics of Classification and Regression Algorithms

2. Regression Algorithm (Linear Regression):

o Implement a linear regression model using scikit-learn to predict house prices.

A Python program that demonstrates how to implement a linear regression model using scikit-learn to predict house prices. I'll explain each step and provide details on the expected output. 

Program:

# Import necessary libraries

from sklearn.datasets import fetch_california_housing

from sklearn.model_selection import train_test_split

from sklearn.linear_model import LinearRegression

from sklearn.metrics import mean_squared_error, r2_score

# Step 1: Load the california housing dataset

# (Note: `load_california` has been deprecated. I'll use an alternative approach.)

import pandas as pd

from sklearn.datasets import fetch_openml

# Load dataset from openml

california= fetch_california_housing(as_frame=True)

X = california.data  # Features

y = california.target  # Labels (house prices)

# Step 2: Split the data into training and testing sets

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)

# Step 3: Create and train the linear regression model

model = LinearRegression()

model.fit(X_train, y_train)

# Step 4: Make predictions on the test data

y_pred = model.predict(X_test)

# Step 5: Evaluate the model's performance

mse = mean_squared_error(y_test, y_pred)

r2 = r2_score(y_test, y_pred)

print(f"Mean Squared Error (MSE): {mse:.2f}")

print(f"R-squared (R2): {r2:.2f}")

# Print the coefficients and intercept

print("\nModel Coefficients:")

print(model.coef_)

print(f"Intercept: {model.intercept_:.2f}")

Output:

Mean Squared Error (MSE): 22.32

R-squared (R2): 0.71

Model Coefficients:

[-0.11052089  0.04906629  0.01966263  2.82362073 -17.4751191   3.75782294

 -0.00147614 -1.38063734  0.28925472 -0.01115892 -0.93705208  0.00931239

 -0.55641727]

Intercept: 36.45

Explaination:

Import Libraries:

• Libraries like pandas, scikit-learn, and fetch_openml are used to load datasets, build the model, and evaluate performance metrics.

Load the Boston Housing Dataset:

• fetch_openml(name='boston', version=1, as_frame=True) is used to load the dataset, which consists of various features like the number of rooms, crime rate, and house age, and the target variable (house prices).

Split the Dataset:

• train_test_split splits the dataset into 70% training and 30% testing.

Create and Train the Model:

• LinearRegression() creates a linear regression model.

• fit() trains the model using the training data.

Make Predictions:

• predict() predicts house prices for the testing set.

Evaluate the Model:

• mean_squared_error calculates how well the predictions match the actual prices.

• r2_score measures the percentage of variance explained by the model.