AlgoAnimator: Interactive Data Structures

Predicting the Future

Linear Regression is the "Hello World" of Machine Learning. It's a statistical method to model the relationship between a dependent variable (like house price) and one or more independent variables (like size).

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1. The Data

Imagine we have data on House Prices. • X-axis: Size (sq ft) • Y-axis: Price ($) We can see a pattern: bigger houses generally cost more.

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2. The Line of Best Fit

We want to draw a straight line through this data that best represents the trend. The equation for a line is: y = mx + b (m = slope, b = intercept)

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3. Measuring Error (Residuals)

How good is our line? We measure the vertical distance from each data point to the line. These are called 'Residuals' or 'Errors'. Our goal: Minimize the sum of these squared errors.

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4. Finding the Best Fit

Using an algorithm like 'Ordinary Least Squares' or 'Gradient Descent', we adjust the Slope (m) and Intercept (b) until the Error is as small as possible.

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5. Making Predictions

Now that we have a trained model, we can predict the price for ANY house size! Drag the slider below to use the model.

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The Math

In Machine Learning terms, we write the linear equation as:

model.py

# Simple Linear Regression

# y = mx + b
# y_pred = weight * input + bias

def predict(x, weight, bias):
    return weight * x + bias

Prediction Function

Cost Function (MSE)

To find the best line, we minimize the Mean Squared Error (MSE).

cost.py

def compute_cost(X, y, weight, bias):
    n = len(y)
    total_error = 0
    
    for i in range(n):
        y_pred = weight * X[i] + bias
        error = (y_pred - y[i]) ** 2
        total_error += error
        
    return total_error / n

Calculating MSE

Gradient Descent

We use the derivatives of the cost function to update our weight and bias iteratively.

optimizer.py

learning_rate = 0.001

# Update rules
weight_gradient = (-2/n) * sum(X * (y - y_pred))
bias_gradient = (-2/n) * sum(y - y_pred)

weight = weight - (learning_rate * weight_gradient)
bias = bias - (learning_rate * bias_gradient)

Updating Parameters