Assume that assumptions SR1-SR6 hold for the simple linear regression model, \(y_{i}=\beta_{1}+\beta_{2} x_{i}+e_{i}\), \(i=1, \ldots, N\). Generally, as the sample size \(N\) becomes larger, confidence intervals become narrower.

a. Is a narrower confidence interval for a parameter, such as \(\beta_{2}\), desirable? Explain why or why not.

b. Give two specific reasons why, as the sample size gets larger, a confidence interval for \(\beta_{2}\) tends to become narrower. The reasons should relate to the properties of the least squares estimator and/or interval estimation procedures.