Multiple linear regression with lm() in R, why is the intersection dependent on the name of the "first" country I have a question about the function lm() used for multiple linear regression analysis.
Context: We have a dataset (that I cannot share) where $y$ is the proportion of women (in some context that I cannot share), then we have some independent variables $x_i$ (numerical values).
Hence I make the command line lm(y~x_1 + x_2 + … +x_n, data = dataset) and that works well. I get a point of intersection n, + more.
However, the dataset allows us to use country as independent variable. For each country at least five points for each independent variable exists. Our hypothesis is that we have a global trend, however er would like to allow for cultural differences in offset. Thus, we are aiming for the model:
y_{country} = a + ( \sum_i  b_i * x_{i,country}) 
    + \epsilon_{country}

Thus, we have the command line lm(y ~ country + x_1 + x_2 + … +x_n, data = dataset).
Problem: My problem is that is seems that the analysis is then dependent on the country that comes first in the alphabet i.e., Australia. In the example with Australia, I get a point of intersection a. But if I change the name of Australia to ex BB, then the output is dependent on Austria instead, and the value of the point of intersection a’ is different from a.
Questions: My questions are: why is the point of intersection dependent on the “first” country? Is there a way to change this? Preferably I would like the “base” intersection of the country specific analysis to be n, and then the (output) list gives the country specific difference from the base intersection (n-a).
I hope my question is clear, and I am sorry, but I cannot share my data with you.

Apart from changing the reference level with relevel, as suggested by akshaymoorthy, there are two other ways of changing the interpretation of the intercepts per factor level:

*

*Remove the intercept from the formula. lm will then   silently add a dummy variable for the reference level, which effectively results in an absolute intercept value per factor level:

.
> library(MASS)
> coef(lm(Gas ~ Temp +Insul+0, whiteside))
       Temp InsulBefore  InsulAfter 
  -0.336697    6.551329    4.986124



*Use a different level encoding ("contrasts" in R lingo). For contr.sum, e.g., the reference level is the mean of all intercepts:

.
> x <- whiteside
> contrasts(x$Insul) <- contr.sum(length(levels(x$Insul)))
> coef(lm(Gas ~ Temp +Insul, x))
(Intercept)        Temp      Insul1 
  5.7687264  -0.3366970   0.7826023

