![given the estimated simple linear regression equation given the estimated simple linear regression equation](https://miro.medium.com/max/1200/1*fyFHpax3A7lkMvCrBwQE1Q.png)
As a rule of thumb, if the regression coefficient from the simple linear regression model changes by more than 10%, then X 2 is said to be a confounder. In this case, we compare b 1 from the simple linear regression model to b 1 from the multiple linear regression model. As noted earlier, some investigators assess confounding by assessing how much the regression coefficient associated with the risk factor (i.e., the measure of association) changes after adjusting for the potential confounder. In the multiple linear regression equation, b 1 is the estimated regression coefficient that quantifies the association between the risk factor X 1 and the outcome, adjusted for X 2 (b 2 is the estimated regression coefficient that quantifies the association between the potential confounder and the outcome). If we now want to assess whether a third variable (e.g., age) is a confounder, we can denote the potential confounder X 2, and then estimate a multiple linear regression equation as follows: Where b 1 is the estimated regression coefficient that quantifies the association between the risk factor and the outcome. We can estimate a simple linear regression equation relating the risk factor (the independent variable) to the dependent variable as follows:
![given the estimated simple linear regression equation given the estimated simple linear regression equation](https://cdn-images-1.medium.com/max/1600/1*F4JzgiTIUfFePLBj4A_JPw.jpeg)
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. Identifying & Controlling for Confounding With Multiple Linear RegressionĪs suggested on the previous page, multiple regression analysis can be used to assess whether confounding exists, and, since it allows us to estimate the association between a given independent variable and the outcome holding all other variables constant, multiple linear regression also provides a way of adjusting for (or accounting for) potentially confounding variables that have been included in the model. 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. Being an advanced SAS procedure it simply does not stop at giving the intercept values as the output.The multiple linear regression equation is as follows:
#Given the estimated simple linear regression equation code#
The above code also gives the graphical view of various estimates of the model as shown below. When the above code is executed, we get the following result − SELECT invoice, horsepower, length, weight
![given the estimated simple linear regression equation given the estimated simple linear regression equation](http://image.slidesharecdn.com/chap13introtomultipleregression-131031212624-phpapp01/95/chap13-intro-to-multiple-regression-5-638.jpg)
![given the estimated simple linear regression equation given the estimated simple linear regression equation](https://media.cheggcdn.com/media/740/74055684-5c59-43c3-8d60-6625ba3fcd17/image.png)
In the result we see the intercept values which can be used to form the regression equation. The below example shows the process to find the correlation between the two variables horsepower and weight of a car by using PROC REG. Variable_1 and variable_2 are the variable names of the dataset used in finding the correlation. The basic syntax for applying PROC REG in SAS is −įollowing is the description of the parameters used − In SAS the procedure PROC REG is used to find the linear regression model between two variables. If it is then, the estimated regression equation can be used to predict the value of the dependent variable given values for the independent variables. Various tests are then used to determine if the model is satisfactory. A model of the relationship is proposed, and estimates of the parameter values are used to develop an estimated regression equation. Linear Regression is used to identify the relationship between a dependent variable and one or more independent variables.