Linear Regression Analysis

In sklearn, Linear Regression Analysis is a machine learning technique used to predict a dependent variable based on one or more independent variables, assuming a linear relationship.

In simple linear regression, we predict the dependent variable Y using a single independent variable X, fitting the data to a straight line, often called as the regression line. The equation for the line is:

$$ Y = \beta_0 + \beta_1 X + \epsilon $$

• Y: The dependent variable to be predicted.
• β₀: The intercept represents Y’s predicted value when X has no effect.
• β₁: The coefficient measures the relationship between X and Y.
• X: The independent variable used to predict Y.
• ε: The error term representing the difference between the observed and predicted values of Y.

Syntax

Here’s the basic syntax for implementing linear regression analysis in Python:

from sklearn.linear_model import LinearRegression

# Create the model
model = LinearRegression()

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

# Predict the dependent variable
predictions = model.predict(X)  # X is the input for which predictions are to be made

Example

In this example, the dependent variable yis directly proportional to the independent variable X, showing a basic linear regression:

# Import required libraries
import numpy as np
from sklearn.linear_model import LinearRegression
import matplotlib.pyplot as plt

# Sample data (Simple Linear Regression)
# X: Independent variable, y: Dependent variable
X = np.array([1, 2, 3, 4, 5]).reshape(-1, 1)  # Reshaping to 2D array for sklearn
y = np.array([1, 2, 3, 4, 5])

# Create the Linear Regression model
model = LinearRegression()

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

# Make predictions
predictions = model.predict(X)

# Output the results
print(f"Intercept (β₀): {model.intercept_}")
print(f"Coefficient (β₁): {model.coef_[0]}")
print(f"Predictions: {predictions}")

# Plot the data and regression line
plt.scatter(X, y, color='red', label='Data Points')
plt.plot(X, predictions, color='green', label='Regression Line')
plt.xlabel('X')
plt.ylabel('y')
plt.title('Simple Linear Regression')
plt.legend()
plt.show()

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The code outputs the following result:

Intercept (β₀): 0.0
Coefficient (β₁): 1.0
Predictions: [1. 2. 3. 4. 5.]

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