House Price Prediction: A Simple Guide with Scikit-Learn and Linear Regression

Navigate the realm of predictive analytics with simplicity

Regression analysis is a statistical method used to model the relationship between a dependent variable and one or more independent variables. It helps us understand how changes in the independent variables are associated with changes in the dependent variable. Linear regression is a specific type of regression that focuses on linear relationships.

Mathematics of Linear Regression

Linear regression involves fitting a straight line (the regression line) to a set of data points in such a way that the sum of the squared differences between the observed and predicted values is minimized. The equation of the regression line is typically represented as:

Y = mx + b

where (Y) is the dependent variable, (x) is the independent variable, (m) is the slope of the line, and (b) is the y-intercept.

The goal is to find the values of (m) and (b) that best fit the data, often using methods like the least squares approach.

Practical Example in Daily Life

Consider the scenario of predicting house prices based on the size of the house. If we collect data on house sizes and their corresponding prices, we can use linear regression to build a model. The size of the house (independent variable) becomes (x), and the price of the house (dependent variable) becomes (Y). The regression line can then help us predict the price of a house based on its size.

For instance, if the regression equation is (Y = 200x + 50), it suggests that for every additional square meter, the house price increases by $200, and the initial price (when the size is zero) is $50.

Advantages and Disadvantages of Linear Regression

Advantages

• Simplicity: Linear regression is easy to understand and interpret, making it accessible for those without advanced statistical knowledge.
• Interpretability: The coefficients in the regression equation have clear interpretations, making it straightforward to explain the relationship between variables.
• Computational Efficiency: Linear regression can be computationally efficient, especially with large datasets.

Disadvantages

• Assumption of Linearity: Linear regression assumes a linear relationship between variables, and if this assumption is violated, the model may provide inaccurate predictions.
• Sensitivity to Outliers: Outliers in the data can significantly impact the regression line, potentially leading to a skewed model.
• Limited to Linear Relationships: Linear regression is not suitable for capturing complex, nonlinear relationships between variables.

In conclusion, linear regression is a powerful and widely used tool in statistics, providing a simple yet effective way to model and understand relationships between variables. However, users must be mindful of its assumptions and limitations when applying it to real-world scenarios.

Libraries Utilized in This Project

For this project, following libraries will be leveraged to facilitate various aspects of our work:

1. NumPy: For numerical operations and array handling (1.23.5).
2. Pandas: To manipulate and analyze structured data efficiently (1.5.3).
3. Matplotlib: For creating visualizations and plots (3.3.4).
4. Seaborn: To enhance the aesthetics of our visualizations built on top of Matplotlib (0.11.1).
5. Scikit-learn: A comprehensive machine learning library for model building and evaluation (1.2.2).

House Price Prediction using Linear Regression

Embark on a journey through the intricate process of house price prediction using linear regression. This tutorial unfolds with a strategic sequence of steps:

• Data Collection
• Data Preprocessing
• Feature Engineering
• Model Selection
• Model Training
• Model Prediction
• Model Evaluation

Data Collection

To demonstrate linear regression, dataset has been taken from Kaggle. Kaggle offers diverse datasets, helping us understand how the algorithm works in real-world situations. This choice allows for a practical and straightforward exploration of linear regression’s application and effectiveness.

Step 1: Installation of the required libraries

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline

Step 2: Load the dataset

USAhousing = pd.read_csv('USA_Housing.csv')

Data Preprocessing

Utilize the .head() function in Python libraries like Pandas to quickly glimpse the initial rows of the dataset. This provides a snapshot of the data's structure, variable names, and the first few entries.

USAhousing.head()

This step helps in understanding the types of information available and identifying potential issues at the beginning of the dataset.

Employ the .info() function to get a concise summary of the dataset, including data types, non-null counts, and memory usage.

USAhousing.info()

This offers insights into the completeness of the dataset and assists in planning subsequent preprocessing steps.

Leverage the .describe() function to generate descriptive statistics, such as mean, standard deviation, and quartiles, providing a deeper understanding of the numerical features in the dataset.

USAhousing.describe()

These statistics assist in identifying outliers, assessing the spread of data, and guiding decisions on normalization or scaling.

Feature Engineering

Let’s harness the powerful capabilities of Seaborn to craft a heatmap, unveiling the correlations between various features and our target value. This visual exploration will provide insights into the strength and direction of relationships, guiding in understanding how different features influence our target variable.

sns.heatmap(USAhousing.corr())

The heatmap vividly illustrates that each feature exhibits some level of correlation with the target variable. Now, let’s delve deeper by employing scatter plots to visually assess the linear relationships between individual features and the target variable. This exploration will provide a more granular understanding of how each feature contributes to the predictive dynamics of the target variable.

plt.scatter(USAhousing['Avg. Area Income'],USAhousing['Price'])

plt.scatter(USAhousing['Avg. Area House Age'],USAhousing['Price'])

plt.scatter(USAhousing['Avg. Area Number of Rooms'],USAhousing['Price'])

plt.scatter(USAhousing['Avg. Area Number of Bedrooms'],USAhousing['Price'])

plt.scatter(USAhousing['Area Population'],USAhousing['Price'])

Now, let’s broaden our perspective by examining a pairplot, offering a comprehensive overview of relationships across multiple features. Additionally, we’ll delve specifically into the distribution of the ‘price’ feature using a distplot, providing a focused insight into its statistical characteristics.

sns.pairplot(USAhousing)

sns.distplot(USAhousing['Price'])

Model Selection

Linear regression is frequently employed for house price prediction due to its simplicity and interpretability. The algorithm assumes a linear relationship between input features (such as square footage, number of bedrooms) and the target variable (house price). This simplicity allows for straightforward interpretation of coefficients, providing insights into how each feature influences the predicted price. Additionally, linear regression is computationally efficient, making it suitable for predicting continuous values like house prices. While the real world may have complex interactions, linear regression serves as a solid starting point for capturing and understanding fundamental relationships in house price data.

Model Training

In the context of house price prediction using linear regression, the model training process involves utilizing a portion of the dataset to train the model on the relationships between the input features (such as square footage, number of bedrooms) and the target variable (house price).

Step 1: Getting the values of independent and dependent variables.

X = USAhousing[['Avg. Area Income', 'Avg. Area House Age', 'Avg. Area Number of Rooms',
               'Avg. Area Number of Bedrooms', 'Area Population']]
y = USAhousing['Price']

Step 2: Splitting the Data

from sklearn.model_selection import train_test_split

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4, random_state=101)

Step 3: Importing and Training the Model

from sklearn.linear_model import LinearRegression

lm = LinearRegression()

lm.fit(X_train,y_train)

Model Prediction

Once the model is trained, use it to make predictions on the testing set.

predictions = lm.predict(X_test)

plt.scatter(y_test,predictions)

Model Evaluation

Evaluate the model’s performance using appropriate metrics, such as mean squared error (MSE) or R-squared, to assess how well it predicts house prices on the testing set.

from sklearn import metrics

print('MAE:', metrics.mean_absolute_error(y_test, predictions))
print('MSE:', metrics.mean_squared_error(y_test, predictions))
print('RMSE:', np.sqrt(metrics.mean_squared_error(y_test, predictions)))

🥳Congratulations 🥳, House Price Prediction project is now ready!

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