(a) Calculate the least squares estimates of the model y_{i}=\beta_{0}+\beta_{1} x_{i, 1}+\beta_{2} x_{i, 2}+\epsilon_{i} \text { for } i=1, \ldots, n (b) Calculate an unbiased estimate for the variance of

the random errors. (C) Calculate a 95% confidence interval for B2. The following are the design matrix a, response vector Y, and(x'x)^-1 for a multiple linear regression model. (d) Briefly explain an implication of the O's in the (x'x)^-1 matrix. The following are the design matrix a, response vector Y, and(z'æ)- for a multiple linear regression model.