Linear Regression & Sensor Calibration Models

Why Machine Learning Matters in Engineering

Physical sensors—such as strain gauges, thermocouples, and pressure transducers—produce noisy voltage readings that must be mapped to true physical quantities using calibrated mathematical models.

Practical Tip Linear Calibration Model ($\hat{y} = w x + b$) A linear regression model learns the optimal sensitivity slope $w$ (weight) and zero-offset intercept $b$ (bias) that minimize Mean Squared Error (MSE) across calibration measurements.

Step-by-Step Worked Example

Run the Python script below to evaluate predictions and compute the Mean Squared Error (MSE) for a transducer calibration curve:

inputs = [1.0, 2.0, 3.0, 4.0]
measured = [3.1, 4.9, 7.2, 8.8]
weight = 2.0
bias = 1.0

predictions = [weight * x + bias for x in inputs]
mse = sum((y_hat - y) ** 2 for y_hat, y in zip(predictions, measured)) / len(inputs)
print("Predictions:", [round(p, 2) for p in predictions])
print(f"Mean Squared Error (MSE): {mse:.4f}")

Real-World Engineering Application

Before deploying a predictive maintenance model on rotating machinery, always inspect residuals and verify that the slope $w$ matches physical sensitivity units.