cobbd <- read.table("http://www.stat.ufl.edu/~winner/data/cobbdoug1.dat", header=F, col.names=c("year","production","capital","labor")) attach(cobbd) n <- length(year) logprod <- log(production) logcap <- log(capital) loglab <- log(labor) Y <- logprod X <- cbind(rep(1,n),logcap,loglab) (betahat <- solve(t(X) %*% X) %*% t(X) %*% Y) Kp <- matrix(c(0,1,1), ncol=3) m <- 1 XPXI <- solve(t(X) %*% X) (SS_ERR <- t(Y) %*% (diag(n) - X %*% XPXI %*% t(X)) %*% Y) (MS_ERR <- SS_ERR / (n - ncol(X))) (Q <- t(Kp %*% betahat - m) %*% solve(Kp %*% XPXI %*% t(Kp)) %*% (Kp %*% betahat - m)) (F_obs <- Q / (nrow(Kp) * MS_ERR)) (F_crit <- qf(.95,nrow(Kp),n-ncol(X))) (P_value <- 1-pf(F_obs,nrow(Kp),n-ncol(X)))