Relationship between two numerical variables

A scatterplot, correlation coefficient and least squares line summarise the relationship between two numerical variables, Y and X. However interpreting the observed relationship is not always straightforward.

The observed relationship may be distorted by the effect of other variables that are correlated with both Y and X, and can give a misleading impression of how the two variables are related.

Marginal and conditional relationships

If the marginal relationship between X and Y is different from their conditional relationship given Z, but Z has either not been recorded or is ignored when analysing the data, then Z is called a lurking variable (or a hidden variable).

Always think about whether there might be a lurking variable, Z, that is distorting the relationship that is observed between Y and X.

Reading ability and height

Nutrition and exam performance