Multiple regression extends simple linear regression to allow for multiple independent (X) variables. This is useful in several contexts:
•To assess the impact of one variable after accounting for others. Does a treatment work after accounting for age differences between the patients who received the treatment and those who received a placebo? Does an environmental exposure increase the risk of a disease after taking into account other differences between people who were and were not exposed to that risk factor?
•To create an equation for making predictions. Given the data we know now, what is the chance that this particular man with chest pain is having a myocardial infarction (heart attack)?
•To understand how changes in several variables contribute to explaining an outcome of interest. For example, how do the concentrations of high-density lipoproteins (HDL, good cholesterol), low-density lipoproteins (LDL, bad cholesterol), triglycerides, C-reactive protein, and homocysteine predict the risk of heart disease? One goal might be to generate an equation that can predict the risk for an individual. Another goal is to understand the contributions of each risk factor in order to aid public health efforts and help prioritize research projects.