Multiple regression is a technique used to study the relationship between an outcome variable and a set of explanatory or predictor variables, and is usually applied when the dependent variable is measured on a continuous scale.
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To illustrate the ideas of multiple regression, we will consider a research problem of assessing the evidence for gender discrimination in legal firms. Statistical modelling can provide the following:
A quantitative assessment of the size of the effect; e.g. the difference in salary between women and men is £5000 per annum;
A quantitative assessment after taking account of other variables; e.g. a female worker earns £6500 less after taking account of years of experience. This conditioning on other variables distinguishes multiple regression modelling from simple ‘testing for differences’ analyses.
A measure of uncertainty for the size of the effect; e.g. we can be 95% confident that the female-male difference in salary in the population from which our sample was drawn is likely to lie between £4500 and £5500.
We can use regression modelling in different modes:
as description (what is the average salary for men and women?),
as part of causal inference (does being female result in a lower salary?), and