do you mean x values instead of x variables? or did you really have 50 x variables in your first model?
why do you think it would stay the same?
please help me with this proof,
I had to do a linear regression of y on x, where the x variables are 1851 to 1900 inclusive.
I was asked to change x varaibles to 1 to 50 inclusive and whether that would change beta one.
i know beta one would stay the same, but how would I be able to prove it?
thanks in advance!!
oh wait i mininterpreted your question, my bad. if you're asking about the transformation:
x' = x - 1850
You know (i hope!) the formula for beta 1, so just show that Var(X) and Cov(X,Y) dont change.
ie, show that
Cov(X',Y) = Cov(X,Y)
Var(X') = Var(X)
i'll use "b" instead of beta 1 to save typing
Define X' = X - 1850
If we run a regression using X', we will get
substitute X' = X - 1850
You should know or be able to prove that . Substitute that in:
Which is the required result.