We have 2008 data on \(y=\) income per capita (in thousands of dollars) and \(x=\) percentage of the population with a bachelor's degree or more for the 50 U.S. states plus the District of Columbia, a total of \(N=51\) observations. We have results from a simple linear regression of \(y\) on \(x\).

a. The estimated error variance is \(\hat{\sigma}^{2}=14.24134\). What is the sum of squared least squares residuals?

b. The estimated variance of \(b_{2}\) is 0.009165 . What is the standard error of \(b_{2}\) ? What is the value of \(\sum\left(x_{i}-\bar{x}\right)^{2} ?\)

c. The estimated slope is \(b_{2}=1.02896\). Interpret this result.

d. Using \(\bar{x}=27.35686\) and \(\bar{y}=39.66886\), calculate the estimate of the intercept.

e. Given the results in (b) and (d), what is \(\sum x_{i}^{2}\) ?

f. For the state of Georgia, the value of \(y=34.893\) and \(x=27.5\). Compute the least squares residual, using the information in parts (c) and (d).