Linear Regression Sandbox App
The Linear Regression Sandbox App offers a hands-on way to understand how linear regression works, and how the gradient descent algorithm is used to optimize the model. The app includes real-time visualizations, user controls, and various interactive elements to explore the effects of different parameters on the model's behavior. The goal of the app is to demonstrate how a linear regression model can fit a line through a set of data points and how the optimization process iteratively improves the line using gradient descent.
Features
Interactive Scatter Plot with Regression Line:
○ The app presents an interactive scatter plot where users can visualize data points on a graph.
○ A regression line (the best-fit line) is drawn on top of the scatter plot, representing the model's predictions.
Live Gradient Descent Visualization:
○ As users start the training process, the app visually demonstrates how gradient descent works. It shows how the regression line updates in each iteration as the algorithm attempts to minimize the loss (the difference between predicted values and actual data points).
Residual Lines:
○ Residuals are the differences between the observed data points and the values predicted by the regression line.
○ Residual lines are shown in real time, allowing users to see how the errors change as the model iteratively improves.
Real-Time Statistics:
○ Iterations: The number of steps taken by the gradient descent algorithm.
○ Loss: A measure of how well the model is fitting the data, with a lower loss indicating a better fit.
○ Slope and Intercept: The parameters of the regression line, which represent the model's equation.
User Controls:
○ Resetting Data Points: Users can generate new random data points, allowing them to experiment with different datasets and see how the regression line changes.
○ Start/Stop Training: Users can start or stop the gradient descent process, providing control over the optimization process.
○ Adjusting Learning Rate: The learning rate controls how big each step of the gradient descent is. A higher learning rate leads to faster convergence (but might overshoot), while a lower learning rate makes the optimization slower but more precise.
○ Toggling Residual Lines: Users can toggle the visibility of residual lines to focus on the regression line itself or to better understand prediction errors.
Click on the picture to go to the app.
This app serves as both an educational tool and a practical demo of how linear regression works. It lets users experiment with data, understand the mechanics of gradient descent, and visualize the effects of different parameters in real time.