AdvancedTopic 87 of 104Engineering Mathematics
Regression analysis
Fits relationships between variables and quantifies prediction error.
In depth
Linear regression fits y=β₀+β₁x by least squares. R² measures the fraction of variance explained, and residual plots check assumptions. Multiple regression uses several predictors, and polynomial or nonlinear forms capture curvature.
Key points
- Correlation is not causation
- Avoid extrapolation beyond data
- Check residuals for patterns
ExampleFitting thermistor resistance against temperature to build a calibration curve.
Regression models relationships between variables and quantifies how well a model predicts, which underpins calibration, forecasting and performance analysis.
What is Regression analysis?
Fits relationships between variables and quantifies prediction error.
Why is it important to understand regression analysis?
Regression models relationships between variables and quantifies how well a model predicts, which underpins calibration, forecasting and performance analysis.
What does R squared tell me?
It is the fraction of variation in the output explained by the model. A high value does not prove the model is correct, so check residuals too.
Why is correlation not causation?
Two variables can move together because of a third factor or chance. Causal claims need controlled experiments or strong physical reasoning.
How is Regression analysis used in practice?
Typical applications include fitting a model of energy use against outdoor temperature, predicting the stress at failure from material composition data and calibrating a flow meter against a reference standard.
What should I learn before Regression analysis?
Study "Hypothesis testing" first (topic 86 of 104 in Engineering Mathematics). It covers the groundwork this topic builds on.
What are the key points of Regression analysis?
Correlation is not causation. Avoid extrapolation beyond data. Check residuals for patterns.
Can you give an example of Regression analysis?
Fitting thermistor resistance against temperature to build a calibration curve.
What comes after Regression analysis?
The next topic is "Reliability and failure distributions", which builds directly on this one.
How difficult is Regression analysis?
It is classed as Advanced in Engineering Mathematics (topic 87 of 104). It is an advanced topic. It assumes you are comfortable with the intermediate topics in Engineering Mathematics.