1.4 Uses of regression

1.: Description. Summarising how \(y\) changes with \(x\), for example by how much mean sales rise for each extra dollar of advertising.
2.: Prediction and forecasting. Estimating \(y\) for a value of \(x\) that has not been observed, within the range of the data.
3.: Control. Choosing \(x\) to give a desired value of \(y\), for example the advertising spend needed for a sales target.
4.: Estimation of parameters that have a scientific meaning, such as a rate of reaction.

Remark. Regression establishes association, not causation. A strong relationship between \(x\) and \(y\) in observational data may be due to a third variable that drives both. Only a designed experiment, in which \(x\) is set by the investigator, supports a causal conclusion.

The name has a history. Francis Galton, studying the heights of parents and their children in the 1880s, found that children of unusually tall parents were on average shorter than their parents, and children of unusually short parents taller: their heights “regressed” towards the mean. The method he used to describe this kept the name.

[next] [prev] [prev-tail] [front] [up]

Questions on this section

Stuck on something here? Ask below and it stays attached to this topic.