Now that you know more about the underlying assumptions of linear regression. We can move forward to continue to build our regression models by adding more variables that might help us to better understand our quantitative response variable. When we add additional explanatory variables to our linear regression, we are now analysing what is called a multiple regression model. When we have multiple explanatory variables in a multiple regression model, this allows us to examine the association between each explanatory variable and the response variable while controlling for the other explanatory variables in the model. Specifically, what this means is that we can examine the association between our explanatory variable of interest and the response variable when all other variables are held constant at a value of zero. The regression coefficient's then, tells us the change in the response variable with a one unit change in our explanatory variable. When all other variables are held constant at a value of zero. But what happens if a quantitative explanatory variable doesn't have a value of zero in it's range of values. For example, say we have a variable age which ranges from 18 to 25. In this case, none of the observations in our data set will have an age equal to zero. 0 is not a meaningful value. This makes our regression coefficients more difficult to interpret because what does it mean when we hold age constant at a value of 0 if there is no value of 0 in the data set for age? Likewise, if we have a categorical variable, for example gender, that is coded 1 for males and 2 for females, what does it mean to hold gender constant at a value of 0? Clearly, we have to either recode or transform our variables so that each variable includes a value of 0 that is meaningful. So how do we do this? It's pretty simple for a categorical variable, because we can just recode one of the categories to be equal to 0. So, in the case of gender, which is coded 1 = Male and 2 = Female, we can simply just recode the variables so 1 = Male and 0 = Female. Then, we were looking at the association between another explanatory variable and response variable when gender is female. In order to give quantitative explanatory variables a meaningful value for zero, we have to center them. Centering involves subtracting the mean of the variable, from the actual value of the variable, for each for each observation. By doing so, we are recording the variable so that the Mean is equal to 0. Then, in a multiple regression model, we can look at the association between another explanatory variable and the In the response variable while holding age constant at its mean. It is important to note that we only center explanatory variables. We do not center the response variable. Centering quantitative variables, also has some very useful properties that we will see later on when we talk about testing non linear associations in our aggression models. Next, we will show you how to write the code to center quantitative variables using an example.