Question: [11 points] Consider the following data, where all summations are over the index i:

Following the example of week 6 lecture note at page 6:

Our formula for the slope coefficient is

Our formula for the intercept coefficient is

The predicted regression is

1. Use your results from above information to complete the following table, putting the sums in the last row. 3 pts
   
2. Show \(\bar{Y}\) that in two difference ways, \(\bar{Y}={{b}_{0}}+{{b}_{1}}\bar{X}\) and \(\bar{Y}=\frac{\sum{{\hat{Y}}}}{N}\) to see if the same?
3. Compute \({{\hat{\sigma }}^{2}}\) ? 3 pts
4. Compute \(\operatorname{var}\left( {{b}_{1}} \right)\) and the standard error of \({{b}_{1}}\), \(SE\left( {{b}_{1}} \right)\) ? 3 pts

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