\text { 1. For the Linear Model } Y-X \beta+c \text {, define } X \text { and } \beta \text { as: }

(a) Find the least squares estimator of ß. (b) Find the mean, variance, and distribution of the least squares estimator from part(₂) (c) Find the estimator of o². \text { (d) Give the formula for the }(1-\alpha) \% \text { confidence interval for } \beta_{1} \text {. }