Which of the following assumptions is NOT necessary for the linear regression model? 0 Normally distributed errors. 0 Independent errors. 0 errors have constant variance. 0 errors have zero mean. Recall the SAT data introduced in lecture, where the response was the sate-average SAT math score, and the predictors were expend, ratio, salary, and takers. To compare the two models with predictors {expend, ratio} and {expend, salary, takers] respectively, which of the following methodsfcriteria can NOT be applied? 0 Cross validation O BIC O F-test O AIC Suppose that our R workspace has a design matrix X, which has 20 rows and 3 columns, which are linearly independent. Also suppose that our R workspace has a 20 entry measured response vector y, which is assumed to be a realization of the random vector Y = XB+ (61, . ..,=20)'s where B = (81, 82, 83)' is an unknown regression coefficient vector and 61, ..., 620 are iid with mean zero and unknown variance o?. Let B = (81, 82, 83)' be the least squares estimator of B. Which of the following R code computes and prints an estimate of sd(B2)? O reps=1e4 estimated. sd=numeric(reps) qrx=qr(x=x) for(r in 1: reps) y=XX*%beta + rnorm(n=20, mean=0, sd=sigma) beta. hat=qr . coef(qrX, y=y) estimated . sd[r]=sqrt(sum((y-Xx*%beta. hat[2])^2)/17) print(estimated. sd) O beta. hat=qr . coef(qr(X), y=y) residuals=y-XX*%beta. hat rss=sum(residuals^2) sigma . hat=sqrt(rss/17) XtX_22=crossprod(X) [2, 2] estimated. sd = sigma. hat*sqrt(1/XtX_22) print(estimated. sd) O reps=1e4 estimated. sd=numeric(reps) qrx=qr(x=x) for(r in 1: reps) y=XX*%beta + rnorm(n=20, mean=0, sd=sigma) beta. hat=qr . coef(qrX, y=y) estimated. sd[r]=sqrt(sum((y-xx*%beta. hat[2])^2)/19) 3 print(estimated. sd) O beta. hat=qr . coef(qr(X), y=y) residuals=y-Xx*%beta. hat rss=sum(residuals^2) Sigma . hat=sqrt(rss/17) XtXinv=qr . solve(crossprod(X)) estimated. sd = sigma. hat*sqrt(XtXinv[2, 2]) print(estimated. sd)