Suppose that we have fit the straight-line regression model $\hat{y}=\hat{\beta}_{0}+\hat{\beta}_{1} x_{1}$ but the response is affected by a second variable $x_{2}$ such that the true regression function is \[E(y)=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}\]

a. Is the least-squares estimator of the slope in the original simple linear regression model unbiased?

b. Show the bias in $\hat{\beta}_{1}$.