Applying Linear Regression to the Real Dataset

Lesson Introduction

Hi there! Today, we're going to learn how to apply Linear Regression to a real dataset. Working with real data shows us how machine learning solves real problems. We'll use the California Housing Dataset . By the end of this lesson, you'll know how to use Linear Regression on a real dataset and understand the results.

Understanding the California Housing Dataset

Before diving into the code, let's understand the dataset we'll be working with. The California Housing Dataset is based on data from the 1990 California census. It contains information about various factors affecting housing prices in different districts of California. Here's a quick overview of the columns in the dataset: MedInc : Median income in block group HouseAge : Median house age in block group AveRooms : Average number of rooms per household AveBedrms : Average number of bedrooms per household Population : Block group population AveOccup : Average household size Latitude : Block group latitude Longitude : Block group longitude MedHouseVal : Median house value for California districts (This is our target variable)

Loading and Preparing the Data: Part 1

First, let's load our data. Think of this step as getting all the ingredients ready before cooking. Here's the code to load the dataset: Python import numpy as np import pandas as pd from sklearn.datasets import fetch_california_housing # Load the California Housing dataset california = fetch_california_housing(as_frame=True) df = california.frame print(df.head()) # Display the first five rows # Output: # MedInc HouseAge AveRooms AveBedrms Population AveOccup Latitude Longitude MedHouseVal # 0 8.3252 41.0 6.984127 1.023810 322.0 2.555556 37.88 -122.23 4.526 # 1 8.3014 21.0 6.238137 0.971880 2401.0 2.109842 37.86 -122.22 3.585 # 2 7.2574 52.0 8.288136 1.073446 496.0 2.802260 37.85 -122.24 3.521 # 3 5.6431 52.0 5.817352 1.073059 558.0 2.547945 37.85 -122.25 3.413 # 4 3.8462 52.0 6.281853 1.081081 565.0 2.181467 37.85 -122.25 3.422 We used the fetch_california_housing function to load the dataset and convert it to a Pandas DataFrame for easier handling.

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Python

# Drop rows with missing values
df.dropna(inplace=True)

# Select the features (all except the target column)
X = df.drop(columns=['MedHouseVal'])

# Select the target column
y = df['MedHouseVal']

print(X.head())
# Output:
#    MedInc  HouseAge  AveRooms  AveBedrms  Population  AveOccup  Latitude  Longitude
# 0  8.3252      41.0  6.984127   1.023810      322.0  2.555556     37.88    -122.23
# 1  8.3014      21.0  6.238137   0.971880     2401.0  2.109842     37.86    -122.22
# 2  7.2574      52.0  8.288136   1.073446      496.0  2.802260     37.85    -122.24
# 3  5.6431      52.0  5.817352   1.073059      558.0  2.547945     37.85    -122.25
# 4  3.8462      52.0  6.281853   1.081081      565.0  2.181467     37.85    -122.25

print(y.head())
# Output:
# 0    4.526
# 1    3.585
# 2    3.521
# 3    3.413
# 4    3.422
# Name: MedHouseVal, dtype: float64

# Drop rows with missing values
df.dropna(inplace=True)

# Select the features (all except the target column)
X = df.drop(columns=['MedHouseVal'])

# Select the target column
y = df['MedHouseVal']

print(X.head())
# Output:
#    MedInc  HouseAge  AveRooms  AveBedrms  Population  AveOccup  Latitude  Longitude
# 0  8.3252      41.0  6.984127   1.023810      322.0  2.555556     37.88    -122.23
# 1  8.3014      21.0  6.238137   0.971880     2401.0  2.109842     37.86    -122.22
# 2  7.2574      52.0  8.288136   1.073446      496.0  2.802260     37.85    -122.24
# 3  5.6431      52.0  5.817352   1.073059      558.0  2.547945     37.85    -122.25
# 4  3.8462      52.0  6.281853   1.081081      565.0  2.181467     37.85    -122.25

print(y.head())
# Output:
# 0    4.526
# 1    3.585
# 2    3.521
# 3    3.413
# 4    3.422
# Name: MedHouseVal, dtype: float64

Python

from sklearn.linear_model import LinearRegression

# Initialize the linear regression model
model = LinearRegression()

# Train the model
model.fit(X, y)

from sklearn.linear_model import LinearRegression

# Initialize the linear regression model
model = LinearRegression()

# Train the model
model.fit(X, y)

Python

# Make predictions
y_pred = model.predict(X)
print(y_pred[:5])  # Display the first five predictions
# Output:
# [4.13642691 3.62014328 3.39896532 3.41478061 3.92649121]

# Make predictions
y_pred = model.predict(X)
print(y_pred[:5])  # Display the first five predictions
# Output:
# [4.13642691 3.62014328 3.39896532 3.41478061 3.92649121]

Python

# Display the intercept
print(f"Intercept: {model.intercept_}")
# Display the coefficients
coefficients = pd.DataFrame(model.coef_, X.columns, columns=['Coefficient'])
print(coefficients)
# Output:
# Intercept: -36.94192020749747
#             Coefficient
# MedInc       0.447808
# HouseAge     0.011540
# AveRooms     0.080079
# AveBedrms   -0.144893
# Population  -0.000046
# AveOccup    -0.004605
# Latitude    -0.426464
# Longitude   -0.430478

# Display the intercept
print(f"Intercept: {model.intercept_}")
# Display the coefficients
coefficients = pd.DataFrame(model.coef_, X.columns, columns=['Coefficient'])
print(coefficients)
# Output:
# Intercept: -36.94192020749747
#             Coefficient
# MedInc       0.447808
# HouseAge     0.011540
# AveRooms     0.080079
# AveBedrms   -0.144893
# Population  -0.000046
# AveOccup    -0.004605
# Latitude    -0.426464
# Longitude   -0.430478

Python

from sklearn.metrics import mean_squared_error

# Calculate the Mean Squared Error
mse = mean_squared_error(y, y_pred)
print(f"Mean Squared Error: {mse:.4f}")  # Mean Squared Error: 0.5308

from sklearn.metrics import mean_squared_error

# Calculate the Mean Squared Error
mse = mean_squared_error(y, y_pred)
print(f"Mean Squared Error: {mse:.4f}")  # Mean Squared Error: 0.5308

Python

# Drop rows with missing values
df.dropna(inplace=True)

# Select the features (all except the target column)
X = df.drop(columns=['MedHouseVal'])

# Select the target column
y = df['MedHouseVal']

print(X.head())
# Output:
#    MedInc  HouseAge  AveRooms  AveBedrms  Population  AveOccup  Latitude  Longitude
# 0  8.3252      41.0  6.984127   1.023810      322.0  2.555556     37.88    -122.23
# 1  8.3014      21.0  6.238137   0.971880     2401.0  2.109842     37.86    -122.22
# 2  7.2574      52.0  8.288136   1.073446      496.0  2.802260     37.85    -122.24
# 3  5.6431      52.0  5.817352   1.073059      558.0  2.547945     37.85    -122.25
# 4  3.8462      52.0  6.281853   1.081081      565.0  2.181467     37.85    -122.25

print(y.head())
# Output:
# 0    4.526
# 1    3.585
# 2    3.521
# 3    3.413
# 4    3.422
# Name: MedHouseVal, dtype: float64

Python

from sklearn.linear_model import LinearRegression

# Initialize the linear regression model
model = LinearRegression()

# Train the model
model.fit(X, y)

Python

# Make predictions
y_pred = model.predict(X)
print(y_pred[:5])  # Display the first five predictions
# Output:
# [4.13642691 3.62014328 3.39896532 3.41478061 3.92649121]

Python

# Display the intercept
print(f"Intercept: {model.intercept_}")
# Display the coefficients
coefficients = pd.DataFrame(model.coef_, X.columns, columns=['Coefficient'])
print(coefficients)
# Output:
# Intercept: -36.94192020749747
#             Coefficient
# MedInc       0.447808
# HouseAge     0.011540
# AveRooms     0.080079
# AveBedrms   -0.144893
# Population  -0.000046
# AveOccup    -0.004605
# Latitude    -0.426464
# Longitude   -0.430478

Python

from sklearn.metrics import mean_squared_error

# Calculate the Mean Squared Error
mse = mean_squared_error(y, y_pred)
print(f"Mean Squared Error: {mse:.4f}")  # Mean Squared Error: 0.5308

Lesson Introduction

Understanding the California Housing Dataset

Loading and Preparing the Data: Part 1

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Loading and Preparing the Data: Part 2

Initializing and Training the Model

Making Predictions

Understanding the Model Outputs

Evaluating the Performance

Lesson Summary