Multiple linear regression: accounting for multiple simultaneous determinants of a continuous dependent variable.

In many cardiovascular experiments and observational studies, multiple variables are measured and then analyzed and interpreted to provide biomedical insights. When these data lend themselves to analyzing the association of a continuous dependent (or response) variable to 2 or more independent (or predictor) variables, multiple regression methods are appropriate. Multiple regression differs from ANOVA, in which the predictors are represented as “factors” with multiple discrete “levels.” In this report, we focus on multiple regression to analyze data sets in which the response variable is continuous; other methods, such as logistic regression and proportional hazards regression, are useful in cases in which the response variable is discrete.1 Although many studies are designed to explore the simultaneous contributions of multiple predictors to an observed response, the data are often analyzed by relating each of the predictor variables, 1 at a time, to a single response variable with the use of a series of simple linear regressions. However, although 2-dimensional data plots and separate simple regressions are easy to visualize and interpret, multiple regression analysis is the preferred statistical method.1–5 We want to reach correct conclusions not only about which predictors are important and the size of their effects but also about the structure by which multiple predictors simultaneously relate to the response. Often, we also want to know whether the multiple predictors that influence a response or outcome do so independently or whether they interact.6 Finally, although only 1 or 2 predictors may interest us, our analysis often must adjust for other influences (ie, confounding effects). A series of simple regressions cannot accomplish these tasks; if we want to examine the simultaneous effects of multiple predictors on a response, we must use a method that treats them accordingly. Conducting a series of simple regression analyses when multiple regression analysis is called for may lead to erroneous conclusions about the contribution of each of multiple predictor variables because this approach does not account for their simultaneous contributions. As a result, a predictor may be deemed important when it is not, or, conversely, a predictor may appear unrelated to the response when examined alone but relate strongly when considered simultaneously with other predictors.