Stats proof - unbiasedness of b1

[bloynoys]

We are to prove sum(n)(I=1)(k(I))*(x(I)) = 1

Where (k(I))= (x(I)-x(bar))/(sum(n)(j=1)(x(j)-x(bar))^2



Attempt at solution:

I rearranged it to equal:

(1/(sum(n)(j=1)(x(j)-x(bar))^2))*(sum(n)(I=1)(x(I)-x(bar))*x(I))

I don't really know how to proceed. Sorry for the formatting issues, I am on mobile currently.

 

[sunjin09]

everything can be written in terms of \sum_i x_i and \sum_i x_i^2, the rest is straightforward