Recall the SAT data introduced in lecture, where the response was the state-average SAT math score, and the predictors were expend, ratio, salary, and takers. Which of the following subsets of the predictors would have the greatest R-squared in a linear regression model fit to these data? [Hint. You do not need to fit these models to determine the answer]. O {expend, ratio} O {expend, salary} O {expend, ratio, salary} O {ratio, salary}Recall the linear regression model for the corn yield data from lecture, where the response was corn yield and the predictors were nitrogen and nitrogen 2. What should replace the ?? in the following R code that is supposed to compute a 95% prediction interval for the yet-to-be observed corn yield when the nitrogen applied is 200? corn=read . table ("corn. txt") X=cbind(1, corn$nitrogen, corn$nitrogen^2) y=corn$yield beta. hat=qr . coef(qr(X) , y=y) rss=sum( (y - Xx*%beta . hat)^2) sE=sqrt(rss/ (nrow(X) -ncol(X) ) ) XtXinv=qr . solve(crossprod(X) ) xnew=c (1, 200, 200^2) est . mean=sum(beta . hat*xnew) moe=? ? c (est . mean-moe, est . mean+moe) qt (0.975, nrow(X) -ncol(X) ) * sE * sqrt(t(xnew)%*%XtXinv**%x new) [1 ] qt(0.975, nrow(X)-ncol(X) ) * SE * sqrt(1+t(xnew)%*%XtXinv% *%xnew) [1] qt(0.95, nrow(X)-ncol(X) ) * SE * sqrt(t(xnew)%*%XtXinv**%xn ew) [1] O at(0.95, nrow(X)-ncol(X) ) * SE * sqrt(1+t(xnew)%*%XtXinv%*%% xnew) [1 ]Recall the linear regression model for the corn yield data from lecture, where the response was corn yield and the predictors were nitrogen and nitrogen*2. What should replace the ?? in the following R code that is supposed to produce a QQ plot comparing the data percentiles of the observed residuals to the corresponding percentiles of a fitted Normal distribution? corn=read . table ("corn. txt") X=cbind(1, corn$nitrogen, corn$nitrogen^2) y=corn$yield beta . hat=qr . coef(qr (X) , y=y) residuals=?? probs=ppoints(length(residuals) ) resid. percentiles=quantile(residuals, probs) normal . percentiles=qnorm(probs, mean=0, sd=sd(residuals)) plot (normal . percentiles, resid. percentiles) abline (0, 1) O abs (y - X*beta) O rnorm(length(y ) , mean=0, sd=sd(y-XX*%beta. hat) ) y-XX*%beta. hat O O (y-xx*%beta. hat)^2A linear regression model with a 40 row by 5 column design matrix, which has linearly independent columns, was t to a dataset and its residual sum of squares was 22.231551 What is the BIC value for this tted model? 45.22636 There is not enough information given to answer this question. 168.2889 123.3422