Comparative Analysis of Mean Square Loss and Least Square Loss in Modeling a Noisy Sine Curve

This paper compares the Mean Square Error (MSE) and Least Square Error (LSE) loss functions when modeling a noisy sine wave. Utilizing a simple linear regression model implemented in Python on Google Colab, a sine curve corrupted by Gaussian noise is generated. Two models are then fit, one optimizing MSE and the other LSE. Their performance is evaluated using Mean Absolute Error (MAE) and R-squared (R²) metrics. The experimental results offer insights into the efficiency and effectiveness of each loss function in capturing underlying trends within noisy data.