Suppose we have a model for $Y_i \approx N(X_i \beta , \sigma^2). $Show that, for a simple random sample $(x_i,y_i), i=1,2,...,n$ from a population of size $N$, $\hat{B}=\frac{\sum_{i=1}^n x_i y_i}{\sum_{i=1}^n x_i^2}$ is unbiased for the superpopulation parameter $\beta$ if the model is correct.
I am trying to solve this proof with no success. So we are trying to go from $E(\hat{B})$ to $B$? Would we use a normal distribution sample mean starting from $E(\frac{1}{n} x_i \hat{\beta})$? I'm pretty confused so any help would be great. Just generally proving no bias with two parameters per sample would be useful to know.
HINT
If I understand the question correctly, you can think of the $x_i$'s as just constants, i.e. they are not random variables. I.e., think of it this way: in each sample $(x_i, y_i)$, the $x_i$ is measured exactly and the $y_i$ is a normal random variable $\sim N(x_i \beta, \sigma^2)$. If $y_i$ were also a constant (i.e. $\sigma = 0$) then the ratio immediately gives $\beta$, but since $y_i$ is random we can only estimate $\beta$.
For $\hat{B}$ to be unbiased, all your need is $E[\hat{B}] = \beta$. Now that $x_i$'s are constants, it should be easy to evaluate $E[\hat{B}]$ and prove it equals $\beta$.