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Multiple regression is a statistical tool used to derive the value of a criterion from several other independent, or predictor, variables. It is the simultaneous combination of multiple factors to assess how and to what extent they affect a certain outcome.
This technique breaks down when the nature of the factors themselves is of an unmeasurable or pure-chance nature.
Instances of multiple regression abound in real life. For instance, a zonal planner wants to know how the value of houses is affected by factors like the average household income in the area, the house’s square footage, the house’s land acreage and the year it was built. After plotting all these into a system that can perform multiple regression, he finds out that the factors that most affect a house’s selling price are the square footage and average income in the area. Multiple regression may even go further and show him that the high-priced houses are affected by the same two factors to a much larger extent than lower- and medium-priced houses.
Another example is a recruiting firm that tries to determine suitable compensation. It finds that the predictor variables for salary are current salary, the number of people an employee has supervised and the amount of responsibility that employee is given. The firm can use multiple regression to find out that a potential employee's current salary is the single most important determinant of the salary that person will be willing to accept in a new job.
Multiple regression, however, is unreliable in instances where there is a high chance of outcomes being affected by unmeasurable factors or by pure chance. For instance, we cannot accurately use regression to calculate to what extent various factors (state of the economy, inflation, average disposable income, companies' earning forecasts, etc.) will influence the stock market index in exactly 20 years' time. There are simply too many unknowns in the mechanics of these external factors.