feat: add linear regression from scratch closes #2689

exercises/1000_programs/medium/linear_regression_scratch.py

@@ -0,0 +1,25 @@
+def linear_regression(x_values, y_values, learning_rate=0.01, epochs=1000):
+    """
+    Implements Simple Linear Regression using Gradient Descent.
+    This is the foundation of Supervised Learning.
+    """
+    # Initializing weight (m) and bias (b)
+    m, b = 0.0, 0.0
+    n = len(x_values)
+
+    for _ in range(epochs):
+        # Calculating predictions
+        y_pred = [m * x + b for x in x_values]
+
+        # Calculating Gradients
+        dm = (-2/n) * sum(x * (y - yp) for x, y, yp in zip(x_values, y_values, y_pred))
+        db = (-2/n) * sum(y - yp for y, yp in zip(y_values, y_pred))
+
+        # Updating parameters (Gradient Descent)
+        m -= learning_rate * dm
+        b -= learning_rate * db
+
+    return m, b
+
+# Simple Test Case
+# x = [1, 2, 3], y = [2, 4, 6] -> Expected m=2, b=0