Multiple Regression interpretation

#1
y=β0+β1x1+β2x2+β3x3
Price = year + (difference between actual miles and average miles, x-xbar) + (year * difference between actual miles and average miles, year(x-xbar))

I am looking at this regression formula, but I don't understand what is going on. Could someone explain it a bit better to me. Not the idea of multiple regression, but why have x-xbar, and (year(x-xbar)) as independent variables?

Also, I understand how to interpret the partial regression coefficients, but what does
β2x2+β3x3 mean. Not separate, but together. Say something like β2(50)+β3(100350). How do you interpret Price when changing two x at the same time? So, x-xbar= 50, and year(x-xbar)= 2007(50)= 100350. I hope I explained myself clear enough. I've been stuck on this for some time now.
 

noetsi

Fortran must die
#2
The only way you can explain why you have the specific slopes (indpendent variables) you mention is your theory. What basis is provided in the question the model is attached to?

When there is no interaction terms (and you have none) then a change in one independent variable does not effect the relationship between a second IV and the dependent variable. The relationship between any of your IV and the dependent variable remains the same at any level of all the other IV. So your intepretation of Y (which I assume price is) is simply the net effect of the changes in all your IV. And the impact of one IV on price is simply the slope of that IV regardless of what happens to the other IV.