Suppose we have a risk factor or an exposure variable, which we denote X 1 (e.g., X 1=obesity or X 1=treatment), and an outcome or dependent variable which we denote Y. Since multiple linear regression analysis allows us to estimate the association between a given independent variable and the outcome holding all other variables constant, it provides a way of adjusting for (or accounting for) potentially confounding variables that have been included in the model. Multiple regression analysis is also used to assess whether confounding exists. ![]() Controlling for Confounding With Multiple Linear Regression Again, statistical tests can be performed to assess whether each regression coefficient is significantly different from zero. In the multiple regression situation, b 1, for example, is the change in Y relative to a one unit change in X 1, holding all other independent variables constant (i.e., when the remaining independent variables are held at the same value or are fixed). ![]() Each regression coefficient represents the change in Y relative to a one unit change in the respective independent variable. Where is the predicted or expected value of the dependent variable, X 1 through X p are p distinct independent or predictor variables, b 0 is the value of Y when all of the independent variables (X 1 through X p) are equal to zero, and b 1 through b p are the estimated regression coefficients. ![]() The multiple linear regression equation is as follows: ![]() Multiple linear regression analysis is an extension of simple linear regression analysis, used to assess the association between two or more independent variables and a single continuous dependent variable.
0 Comments
Leave a Reply. |