## Regression analysis

One often wishes to explain part of the variation in a result of observation by expressing the result as a function of one or more quantitative variables (explanation variables), see the Figure below. With an explanation variable, z, a linear model is as follows

x = a + b·z + eres

where eres is that part of x which cannot be explained (predicted) by z.

Figure. Explanation (predictive) model.

The parameters in the model – the intercept a and the slope b, as well as the standard deviationof eres are estimated with regression analysis.

It is not necessary for the model that there is a cause relation, but it is important for the interpretation if there is a cause relation or a collective variation caused by a common factor affecting the variables. If there are several affecting factors, then these can give independent effects but may even vary cooperatively, that is the effect of one factor depends on the level of the others.

Regression analysis can for example be used in the investigation of how an influence quantity affects a measurement result, for tests of robustness, and to estimate the contribution to the variation in measurement due to the influence quantity.

Example: Regression