Dear Muawya Ahmed Hussein,

for example, look at the link: 

http://psych.colorado.edu/~carey/qmin/qminChapters/QMIN13-GLM_Multivariate.pdf

You can get more detain on any standard statitics book or regression analysis book. Below, there are some example of multiple regression, hope they will help. Thanks.

http://www.stat.yale.edu/Courses/1997-98/101/linmult.htm

http://cameron.econ.ucdavis.edu/excel/ex61multipleregression.html

http://faculty.cas.usf.edu/mbrannick/regression/Reg2IV.html

You could average the dependent variable at each data point or get the difference which becomes the y variable into your model

See p.566 of the attached. Contact me if you have questions. Best wishes, David

Dear colleague,

What you need is called  "Multivariate Multiple Regression" or just "Multivariate Regression". Please see the link below for more details:

http://www.public.iastate.edu/~maitra/stat501/lectures/MultivariateRegression.pdf

Best wishes.

Dear Mr. Mauvya Ahmed Hussain,

Multiple regression is fine for multiple independent variables. However the question is about multiple dependent variables. The answer is Canonical Correlation. But it all depends on the scales of measurement of the variables, purpose of the study and other factors. A more specific answer is possible only if you elaborate the problem in more detail

In my view a good way to start is to fit a multiple regression model to each response separately. With the learning from this work you can apply multiple response optimization techniques to identify the settings of the predictor variables that will give you the desired values of the responses. This approach will maximize the chances that you will develop useful understanding of the system you are studying.

 The decision of statistical analysis depends on many factors. The data, the measurement models, and other variable characteristics, i.e., parametric vs non-parametric. You can try simultaneous equation modelling techniques. Or you can run two separate regression analyses to estimate two different models (one for each dependent variable). 

You have only two options categorically.