Click4Ai

58.

Easy

Implement the **Root Mean Squared Error (RMSE)** metric.

Formula:

RMSE = sqrt( (1/n) * sum((y_true - y_pred)^2) )

= sqrt(MSE)

Write a function rmse(y_true, y_pred) that takes two arrays and returns the RMSE value.

Example:

y_true = [3, 5, 2, 7]

y_pred = [2.5, 5.5, 2, 8]

MSE = (0.25 + 0.25 + 0 + 1) / 4 = 0.375

RMSE = sqrt(0.375) = 0.6124 (approx)

**Explanation:** RMSE is the square root of MSE. It has the advantage of being in the same units as the target variable, making it more interpretable than MSE.

Constraints:

  • y_true and y_pred are 1D numpy arrays of equal length
  • Return a single float value
  • Do not use sklearn; implement from scratch

    • Test Cases

    Test Case 1
    Input: y_true=[3,5,2,7], y_pred=[2.5,5.5,2,8]
    Expected: 0.6123724356957945
    Test Case 2
    Input: y_true=[1,2,3], y_pred=[1,2,3]
    Expected: 0.0
    Test Case 3
    Input: y_true=[0,0,0], y_pred=[1,1,1]
    Expected: 1.0
    + 2 hidden test cases