Fitting a Linear Regression Model to the Housing Dataset with Sklearn

Introduction and Basics of Linear Regression Model Fitting

Welcome back! Today, we are delving into the practical application of predictive modeling. This lesson will focus on applying Linear Regression using the California Housing Dataset and Python, to make predictions with real-world data. This time we will be utilizing the powerful sklearn library to simplify our process, instead of implementing linear regression from scratch, this will allow us to efficiently calculate coefficients, plot data and regression lines. So, without further ado, let's dive in!

Data Loading and Preparation

X

Fitting the Model

With our data prepared, we can now fit our linear regression model: Python from sklearn.linear_model import LinearRegression # Creating and training the model model = LinearRegression() model.fit(X, Y) Here, we initialize the LinearRegression model and fit it to our data using model.fit(X, Y) . This function trains the model by finding the best coefficients that predict our target values from the given features. It does this through an optimization process, minimizing the error between actual and predicted values. Essentially, model.fit enables us to automate the complex steps of learning from data, allowing sklearn to handle the underlying mathematics. This makes fitting the model both accessible and efficient, readying it for predictions without manual intervention.

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Python

from sklearn.datasets import fetch_california_housing
import matplotlib.pyplot as plt

# Fetching the dataset
housing = fetch_california_housing()

# Selecting the Median Income feature, index 0 represents Median Income
X = housing.data[:, 0]  # Extracting the first column
X = X.reshape(-1, 1)  # Reshape for a single feature (sklearn expects 2D array)
Y = housing.target

Python

# Predictions for the dataset
Y_pred = model.predict(X)

# Plotting actual data points
plt.scatter(X, Y, color='blue')

# Plotting the regression line
plt.plot(X, Y_pred, color='red')

plt.title("Linear Regression on California Housing Dataset")
plt.xlabel('Median Income')
plt.ylabel('Median House Value')
plt.grid(True)
plt.show()

# Predictions for the dataset
Y_pred = model.predict(X)

# Plotting actual data points
plt.scatter(X, Y, color='blue')

# Plotting the regression line
plt.plot(X, Y_pred, color='red')

plt.title("Linear Regression on California Housing Dataset")
plt.xlabel('Median Income')
plt.ylabel('Median House Value')
plt.grid(True)
plt.show()

Python

# Note: sklearn requires input to be a 2D array, thus we convert our single value to 2D using double brackets
x_new = [[8]]  # Median income normalized, representing $80000.00
y_new_pred = model.predict(x_new)
print(f"For a median income of ${x_new[0][0] * 10000:.2f}, the projected median house value is ${y_new_pred[0] * 100000:.2f}")
# Output: For a median income of $80000.00, the projected median house value is $379436.37

Python

# Predictions for the dataset
Y_pred = model.predict(X)

# Plotting actual data points
plt.scatter(X, Y, color='blue')

# Plotting the regression line
plt.plot(X, Y_pred, color='red')

plt.title("Linear Regression on California Housing Dataset")
plt.xlabel('Median Income')
plt.ylabel('Median House Value')
plt.grid(True)
plt.show()

Python

# Note: sklearn requires input to be a 2D array, thus we convert our single value to 2D using double brackets
x_new = [[8]]  # Median income normalized, representing $80000.00
y_new_pred = model.predict(x_new)
print(f"For a median income of ${x_new[0][0] * 10000:.2f}, the projected median house value is ${y_new_pred[0] * 100000:.2f}")
# Output: For a median income of $80000.00, the projected median house value is $379436.37

Introduction and Basics of Linear Regression Model Fitting

Data Loading and Preparation

Fitting the Model

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Data Visualization and Regression Line

Making Predictions

Next Steps: Evaluating Your Model

Lesson Summary