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.

It's a matter of coding within the regression. Since it's a factor variable, R uses dummy coding automatically, using the first level as reference category (if the factor levels are unordered, then it seems like it uses the alphabetically first level, i.e. Australia). I think you can specify contrasts to get a different effect coding, for example the countries' effects compared to the grand mean.
