Estimation using panel data

[ginolveb]

Hello!
I would greatly appreciate your help!

I am testing a panel data for 1 dependent variable (M) and 5 parameters such that N=36countries and T=13years.
Using the fixed method across periods they turn out to be all significant.
Purpose:
-Having obtained the coefficients (5 values) and constant (1 value) for my set of countries, I want to use the coefficients to deduce the value of M for a country outside my data set.
-Having the values of the 5 parameters across the 13years, I am finding M.
Problem:
-I am obtaining very weird results.
Help:
-Do you think I should regress for each period on use different coefficients per period?

Please could you help me?