Hi Joannie, that context sounds like  linear model fiiting or multiple regression approach with dummy variable (groups)

Do you want to compare the effect each independent variable between 2 group ? 

Multiple Linear regression with Dummy variable may help you. 

You may use 11 variable : Dummy + IV1 + IV2 +...+ IV5 + Dummy*IV1 + Dummy*IV2 + ... + Dummy*IV5 

If dummy*IV1 is significant, it mean the effect of IV1 on DV between 2 group is difference.

Hi,

You don't give many details but I think perhaps a partial least square regression might be appropriate. (It's allows to avoid collinearity contrarily to multiple regression)

hello Joannie,

The model or tool you should use depends on the type of your variables particulary the dependent variable. If the dependent variable is numeric and continuous then Multiple Linear regression with Dummy variable might help you. 

Before you decide on an approach, you need to be very clear on your modeling goal.  If the goal is to elucidate apparent functional relationships between the independent variables and the response variable, then MLR is a preferred approach - provided that collinearity between the independent variables is not problematic.  If the goal is simply to use all your independent variables to predict the response  variable, without trying to interpret the meaning of the individual parameter coefficients, then PLS is an option.  In either event, and as the other respondents have said, you can incorporate the effects of population by coding the variable as a dummy variable.  In the case of the MLR modeling, this approach is also known as analysis of covariance (ANCOVA).

With respect to MLR modeling, an arguably better approach than including population as a dummy variable in the model is to use a mixed level modeling (MLM) or hierarchical modeling framework.  MLM modeling will allow you to formally test whether population exerts a significant effect on response as either a random effect (i.e., its effect is only on the intercept and does not influence the functional relationship between the response and independent variables) or a fixed effect (i.e., its effect includes influencing the functional relationship as expressed by slope modifications for some or all of the independent variable relationships with the response variable).  Depending upon the circumstances and how you implement the models, ANCOVA and MLM can yield equivalent or similar results, but MLM is less constrained in its underlying assumptions than ANCOVA.

Some of these answers may be right, but you haven't told us the question you are trying to answer. Without that, we cannot really help. What have you measured? What are the predictor variables? And what is the hypotheses?

Ronan is right - the nature of your data and the questions you are trying to answer will dictate the methodological direction that will best serve your needs.  These questions will also dictate aspects of how the model is constructed.  Regarding methodological direction as an example, if your response variable is a categorical variable rather than a continuous variable, then logistic regression or discriminant analysis will be more appropriate than linear regression.  Or, if your response variable is count data, then other approaches such as poisson regression may be warranted.  Likewise, if you are working with survey data, that suggests a different methodological approach.  My assumption is that, at a minimum (1) your response and independent variables are continuous (other than the population variable) and (2) the functional relationships between your variables are linear, or can be linearized through appropriate transformations.  Even with the above two assumptions in place, there are a multitude of different approaches to consider.  In retrospect, your question is really too open-ended to offer a meaningful answer regarding appropriate methodological choices.

I also agree with Ronan and Curt. It would also hep to specify the nature of your variables - are they continuous or categorical?