Question: Suppose that you obtained the following summary quantities to estimate the parameters in a regression study. Assume that x and y are related according to the simple linear regression model: \[\hat{y}\] = \[{{\hat{\beta }}_{0}}\] + \[{{\hat{\beta }}_{1}}\] x.

n = 14, \[\sum\limits_{i=1}^{n}{{{y}_{i}}}\] = 572, \[\sum\limits_{i=1}^{n}{y_{i}^{2}}\] = 23,530, \[\sum\limits_{i=1}^{n}{{{x}_{i}}}\] = 43, \[\sum\limits_{i=1}^{n}{x_{i}^{2}}\] = 157.42, and \[\sum\limits_{i=1}^{n}{{{x}_{i}}}{{y}_{i}}\] = 1697.80.

a) Calculate the least square estimates of the slope ( \[{{\hat{\beta }}_{1}}\] ) and intercept ( \[{{\hat{\beta }}_{0}}\] ).

b) Estimate the variance of the error term, ?².