Simple linear regression

Learning objectives

• Fit a simple linear regression and interpret slope with units.
• Inspect residuals for validity.
• Avoid extrapolation and causal over-claiming.

Model in plain terms

Y = β0 + β1X + error. β1 is the expected change in Y per one-unit change in X within the fitted range.

Check independence, linearity, constant variance, influential points and residual distribution before trusting the model.

Limits

• Do not extrapolate outside the data range.
• High R² is not proof of causation.
• Prediction intervals are wider than mean-response intervals.

Garment-factory example

Within the validated operating range, model curing temperature (°C) versus dimensional change (%); slope quantifies expected shrinkage per °C.

Method

1. Plot scatter first.
2. Fit in a free spreadsheet.
3. Inspect residual plots.
4. Report slope with units and its CI.

Common mistakes

• Extrapolating outside the data range.
• Interpreting a high R² as causation.