How to do a fixed effects panel regression?

I have searched through textbooks and forums but not seeming to find what I need. I have 20 countries and for each country I have 10 years of profits which are my response variables. I have 4 dependent variables (each with 10years of data). i.e. PROFITS_ jt = a + beta1*X1_ jt +...+ beta4*X4_ jt + error, where j is the country and t is the year. How should I perform a regression? Any help would be appreciated!

Answer 1

[Image Analyst]

Spell out your model in full, because it looks like you have the same X_jt in each term and so your model ends up being

PROFITS_jt =  a + X_jt * (beta1 + beta2 + beta3 + beta4);

which is the same as PROFITS_jt = a + X_jt * b which is trivially solved by polyfit

coefficients = polyfit(X_jt, PROFITS_jt, 1);

so

a = coefficients(2) 
b = coefficients(1)

but I'm not sure what you mean. Why have 4 betas when they all multiply the same X vector?

[A]

Apologies, this was a mistake. I have edited the post - there are 4 separate explanatory variables. Thanks.