Click4Ai

51.

Medium

Implement **Simple Linear Regression** using gradient descent to fit a model of the form **y = wx + b**.

Gradient Descent Update Rules:

dw = (1/n) * sum(2 * x * (w*x + b - y))

db = (1/n) * sum(2 * (w*x + b - y))

w = w - learning_rate * dw

b = b - learning_rate * db

Your class should have:

  • `fit(X, y)`: Train the model using gradient descent for `n_iterations` steps.
  • `predict(X)`: Return predicted values using the learned weight and bias.

    • Example:

    X = [1, 2, 3, 4, 5]

    y = [2, 4, 6, 8, 10] (i.e., y = 2x)

    model = SimpleLinearRegression(learning_rate=0.01, n_iterations=1000)

    model.fit(X, y)

    model.predict([6, 7]) # Should return values close to [12, 14]

    **Explanation:** The model learns weight ~ 2.0 and bias ~ 0.0, fitting the line y = 2x.

    Constraints:

  • Initialize weight and bias to 0
  • Use the provided learning rate and number of iterations
  • X and y are 1D numpy arrays of the same length

    • Test Cases

    Test Case 1
    Input: X=[1,2,3,4,5], y=[2,4,6,8,10]
    Expected: predictions close to y=2x (weight~2.0, bias~0.0)
    Test Case 2
    Input: X=[1,2,3,4,5], y=[3,5,7,9,11]
    Expected: predictions close to y=2x+1 (weight~2.0, bias~1.0)
    Test Case 3
    Input: X=[0,1,2,3], y=[1,1,1,1]
    Expected: predictions close to y=1 (weight~0.0, bias~1.0)
    + 2 hidden test cases