Linear regression with matplotlib / numpy

Linear regression with matplotlib / numpy

You can perform linear regression with Matplotlib and NumPy in Python. Linear regression aims to find the best-fit line for a set of data points. Here's a step-by-step guide to creating a simple linear regression plot:

  1. Import necessary libraries:

    import numpy as np import matplotlib.pyplot as plt

  2. Create sample data:

    Let's create some sample data for demonstration. You can replace this with your own dataset.

    # Sample data x = np.array([1, 2, 3, 4, 5]) y = np.array([2, 3, 4, 5, 6])

  3. Calculate the linear regression parameters:

    Use NumPy's polyfit function to calculate the coefficients of the best-fit line (slope and intercept).

    slope, intercept = np.polyfit(x, y, 1)

  4. Create the regression line:

    Calculate the predicted values for the regression line based on the coefficients.

    regression_line = slope * x + intercept

  5. Create the scatter plot and regression line plot:

    Plot the original data points as a scatter plot and the regression line on the same graph.

    plt.scatter(x, y, label='Data Points') plt.plot(x, regression_line, label='Linear Regression Line', color='red') plt.legend()

  6. Show the plot:

    Display the graph with the data points and the regression line.

    plt.xlabel('X') plt.ylabel('Y') plt.title('Linear Regression with Matplotlib and NumPy') plt.show()

Here's the complete code:

import numpy as np import matplotlib.pyplot as plt # Sample data x = np.array([1, 2, 3, 4, 5]) y = np.array([2, 3, 4, 5, 6]) # Calculate the linear regression parameters slope, intercept = np.polyfit(x, y, 1) # Create the regression line regression_line = slope * x + intercept # Create the scatter plot and regression line plot plt.scatter(x, y, label='Data Points') plt.plot(x, regression_line, label='Linear Regression Line', color='red') plt.legend() plt.xlabel('X') plt.ylabel('Y') plt.title('Linear Regression with Matplotlib and NumPy') plt.show()

This code will create a scatter plot of the sample data points along with the linear regression line that best fits the data. You can replace the x and y arrays with your own dataset for real-world linear regression analysis.

Examples

  1. "How to visualize linear regression with matplotlib and numpy?"

    Description: This query indicates a desire to understand how to plot linear regression using matplotlib and numpy, suggesting the user wants to visualize the regression line along with the data points.

    # Example code: import numpy as np import matplotlib.pyplot as plt # Generate random data for demonstration np.random.seed(0) X = 2 * np.random.rand(100, 1) y = 4 + 3 * X + np.random.randn(100, 1) # Perform linear regression X_b = np.c_[np.ones((100, 1)), X] # Add x0 = 1 to each instance theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y) # Plot data points plt.scatter(X, y) # Plot regression line X_new = np.array([[0], [2]]) X_new_b = np.c_[np.ones((2, 1)), X_new] # Add x0 = 1 to each instance y_predict = X_new_b.dot(theta_best) plt.plot(X_new, y_predict, "r-") plt.xlabel("X") plt.ylabel("y") plt.title("Linear Regression with Matplotlib and Numpy") plt.show()

  2. "Implementing simple linear regression using numpy and matplotlib"

    Description: This query suggests the user is seeking a basic implementation of simple linear regression using numpy and matplotlib, indicating a beginner-level understanding of regression analysis.

    # Example code: import numpy as np import matplotlib.pyplot as plt # Generate sample data X = np.array([1, 2, 3, 4, 5]) y = np.array([2, 3, 4, 5, 6]) # Calculate coefficients of the linear regression line A = np.vstack([X, np.ones(len(X))]).T m, c = np.linalg.lstsq(A, y, rcond=None)[0] # Plot data points plt.scatter(X, y) # Plot regression line plt.plot(X, m*X + c, 'r', label='Fitted line') plt.xlabel('X') plt.ylabel('y') plt.title('Simple Linear Regression with Matplotlib and Numpy') plt.legend() plt.show()

  3. "Visualizing linear regression line with matplotlib and numpy"

    Description: This query suggests the user wants to specifically visualize the linear regression line overlaid on the scatter plot of the data points using matplotlib and numpy.

    # Example code: import numpy as np import matplotlib.pyplot as plt # Generate sample data np.random.seed(0) X = 2 * np.random.rand(100, 1) y = 4 + 3 * X + np.random.randn(100, 1) # Perform linear regression X_b = np.c_[np.ones((100, 1)), X] # Add x0 = 1 to each instance theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y) # Plot data points plt.scatter(X, y) # Plot regression line plt.plot(X, X_b.dot(theta_best), color='red') plt.xlabel("X") plt.ylabel("y") plt.title("Visualizing Linear Regression with Matplotlib and Numpy") plt.show()

  4. "Plotting linear regression line in Python using matplotlib and numpy"

    Description: This query suggests the user is looking for a method to plot the linear regression line in Python, specifically utilizing matplotlib and numpy libraries.

    # Example code: import numpy as np import matplotlib.pyplot as plt # Sample data X = np.array([1, 2, 3, 4, 5]) y = np.array([2, 3, 4, 5, 6]) # Calculate slope and intercept of the regression line slope, intercept = np.polyfit(X, y, 1) # Plot data points plt.scatter(X, y) # Plot regression line plt.plot(X, slope*X + intercept, color='red') plt.xlabel('X') plt.ylabel('y') plt.title('Linear Regression Line with Matplotlib and Numpy') plt.show()

  5. "How to draw a linear regression line on a scatter plot in Python?"

    Description: This query implies the user wants to overlay a linear regression line on a scatter plot in Python, indicating a need for visualization techniques using matplotlib and numpy.

    # Example code: import numpy as np import matplotlib.pyplot as plt # Generate random data np.random.seed(0) X = 2 * np.random.rand(100, 1) y = 4 + 3 * X + np.random.randn(100, 1) # Perform linear regression X_b = np.c_[np.ones((100, 1)), X] # Add x0 = 1 to each instance theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y) # Plot data points plt.scatter(X, y) # Plot regression line plt.plot(X, X_b.dot(theta_best), color='red') plt.xlabel("X") plt.ylabel("y") plt.title("Linear Regression Line on Scatter Plot") plt.show()

  6. "Simple linear regression visualization with matplotlib and numpy"

    Description: This query indicates a focus on a straightforward visualization of simple linear regression using matplotlib and numpy, suggesting the user prefers simplicity in their approach.

    # Example code: import numpy as np import matplotlib.pyplot as plt # Sample data X = np.array([1, 2, 3, 4, 5]) y = np.array([2, 3, 4, 5, 6]) # Calculate regression line parameters slope, intercept = np.polyfit(X, y, 1) # Plot data points plt.scatter(X, y) # Plot regression line plt.plot(X, slope*X + intercept, 'r', label='Fitted line') plt.xlabel('X') plt.ylabel('y') plt.title('Simple Linear Regression Visualization') plt.legend() plt.show()

  7. "How to plot linear regression in Python using numpy and matplotlib?"

    Description: This query indicates a general interest in plotting linear regression in Python, specifically utilizing numpy and matplotlib libraries for visualization.

    # Example code: import numpy as np import matplotlib.pyplot as plt # Sample data X = np.array([1, 2, 3, 4, 5]) y = np.array([2, 3, 4, 5, 6]) # Calculate regression line parameters slope, intercept = np.polyfit(X, y, 1) # Plot data points plt.scatter(X, y) # Plot regression line plt.plot(X, slope*X + intercept, 'r', label='Fitted line') plt.xlabel('X') plt.ylabel('y') plt.title('Linear Regression with Matplotlib and Numpy') plt.legend() plt.show()

  8. "Visualizing linear regression model with matplotlib and numpy in Python"

    Description: This query suggests a desire to visualize a linear regression model using matplotlib and numpy in Python, indicating the user is interested in understanding the relationship between the data and the fitted line.

    # Example code: import numpy as np import matplotlib.pyplot as plt # Sample data np.random.seed(0) X = 2 * np.random.rand(100, 1) y = 4 + 3 * X + np.random.randn(100, 1) # Perform linear regression X_b = np.c_[np.ones((100, 1)), X] # Add x0 = 1 to each instance theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y) # Plot data points plt.scatter(X, y) # Plot regression line plt.plot(X, X_b.dot(theta_best), color='red') plt.xlabel("X") plt.ylabel("y") plt.title("Visualizing Linear Regression Model with Matplotlib and Numpy") plt.show()

  9. "Python code for plotting linear regression line using matplotlib and numpy"

    Description: This query implies a straightforward request for Python code to plot a linear regression line using matplotlib and numpy, suggesting the user is looking for a concise and direct solution.

    # Example code: import numpy as np import matplotlib.pyplot as plt # Sample data X = np.array([1, 2, 3, 4, 5]) y = np.array([2, 3, 4, 5, 6]) # Calculate regression line parameters slope, intercept = np.polyfit(X, y, 1) # Plot data points plt.scatter(X, y) # Plot regression line plt.plot(X, slope*X + intercept, 'r', label='Fitted line') plt.xlabel('X') plt.ylabel('y') plt.title('Linear Regression Line with Matplotlib and Numpy') plt.legend() plt.show()

  10. "Plotting linear regression line on scatter plot using matplotlib and numpy in Python"

    Description: This query specifies the intention to plot a linear regression line on a scatter plot using matplotlib and numpy in Python, suggesting the user is interested in visualizing the relationship between the data points and the fitted line.

    # Example code: import numpy as np import matplotlib.pyplot as plt # Sample data np.random.seed(0) X = 2 * np.random.rand(100, 1) y = 4 + 3 * X + np.random.randn(100, 1) # Perform linear regression X_b = np.c_[np.ones((100, 1)), X] # Add x0 = 1 to each instance theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y) # Plot data points plt.scatter(X, y) # Plot regression line plt.plot(X, X_b.dot(theta_best), color='red') plt.xlabel("X") plt.ylabel("y") plt.title("Linear Regression Line on Scatter Plot") plt.show()

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