Multiple Regression

Real-world outcomes usually depend on several factors. Multiple regression estimates the separate effect of each factor while holding the others constant.

For example, a house price might depend on size, number of bedrooms, location and age. A multiple regression could estimate that, holding the other factors constant, each extra square metre adds about 2,000 to the price, each extra year of age reduces it by about 500 and being in a particular neighbourhood adds about 30,000.

In finance, multiple regression is used to explain investment returns using several risk factors, such as overall market movements, company size and value characteristics, to forecast sales based on price, advertising and economic conditions, and to estimate the drivers of credit risk.

Multiple regression is more powerful than simple regression, but it has its own challenges. If independent variables are closely related to each other, a problem called multicollinearity, it can be hard to separate their individual effects. Adding too many variables can make a model fit past data well but predict poorly. As with all regression, it shows association rather than proof of cause and effect.