Applications of linear regression, Basic Statistics

Linear regression is widely used in biological behavioral and social sciences to describe relationship between variables. It ranks as one of the most important tools used in these disciplines.

1.Medicine: As one example early evidence relating tobacco smoking to mortality and morbidity came from studies employing regression. Researchers usually include several variables in their regression analysis in an effort to remove factors that might produce spurious correlations. For the cigarette smoking example researchers might include socio economic status in additional to smoking to ensure that any observed effect of smoking on mortality is not due to some effect of education or income. However it is never possible to include all possible confounding variables in a study employing regression. For the smoking example a hypothetical gene might increase mortality and also cause people to smoke more. For this reason randomized controlled trains are considered to be more trustworthy than a regression analysis.

2. Finance: Linear regression underlies the capital asset pricing model, and the concept of using beta for analyzing and quantifying the systematic risk of an investment. This comes directly from the beta coefficient of the linear regression model that relates the return on the investment to the return on all risky assets.

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