Muhammad - 

Are you talking about continuous variables here?  I am not familiar with your application, but it sounds like you could use scatterplots to study your data and how it might be modeled. 

If it is as simple as a linear regression through the origin (with 0 user 'density' "predicting" zero energy consumption) then you could estimate standard errors of the prediction errors and you might want to also plot confidence around predictions as in the example at the attached link. 

Your application may be much more complicated, but graphics can help you understand possible relationships. 

Cheers - Jim 

PS - Also, you can obtain estimates for the variance of the prediction error for more complex models. In SAS, for example, the square root of this is STDI in SAS PROC REG. 

Data CRE Prediction 'Bounds' and Graphs Example for Section 4 of ...

Dear Muhammad

A WSN base station could make operation and energy expenses from three sources, A) from WSN nodes information gather or request response process on WSN nodes, B) from internal operation to manage its own management structures, and C) from user request information, or subscriptions. 

A and C could have more communication activities than B and maybe they could be more energy consumption ones.

The user could only affect the C option, if your WSN are not a query driven one, and also depend on if any user use or consume the same amount of information or if any user could have different pattern of information consuming. This fact could make your expression more simple or more complex.

If you need any additional information we can work in this expression. let me know.

Hi Muhammad,

I am assuming you are talking about the power needed by a cell tower base station as a function of the number of users. First think about a two-dimentional random distributing of user locations with respect to the base station. In the simulation, you need to randomize distance and angle of the user from the base station x-y frame of reference. You need to decide what you want for the the distribution function for distance and the distribution function for the angle. Using a uniform distribution for both may be a good first choice. Next, you need to know the algorithm that the base station uses to adjust its transmitted power to the user. This involves measuring the signal to noise ratios for the communication link and setting power so that a low bit error rate is acheived. Next, you need to know the efficiency of the base station transmitter electronics so you can compute input power based on required output power. Randomly adding and subtracting users should give you the estimate you need.

Good luck.