Chapter 11.3, Problem 1E

If ${\hat{\beta }}_0$ and ${\hat{\beta }}_1$ are the least-squares estimates for the intercept and slope in a simple linear regression model, show that the least-squares equation $\hat{y}={\hat{\beta }}_0+{\hat{\beta }}_{1}x$ always goes through the point $(\bar{x},\bar{y})$. [Hint: Substitute $\bar{x}$ for x in the least-squares equation and use the fact that ${\hat{\beta }}_0=\bar{y}-{\hat{\beta }}_1\bar{x}$.]