R : Copyright 2001, The R Development Core Team
Version 1.3.1  (2001-08-31)

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> data <- read.table("data.dat",header=F)
> attach(data)
> Y <- as.matrix(data[,1])
> X <- as.matrix(cbind(1, data[,2:ncol(data)]))
> XTX <- t(X) %*% X
> XTXINV <- solve(XTX)
> XTY <- t(X) %*% Y
> betahat <- XTXINV %*% XTY
> Xbetahat <- X %*% betahat
> sigsq <- as.vector(t(Y - Xbetahat) %*% (Y - Xbetahat) / (nrow(X) - ncol(X)))
> VCOV <- sigsq * XTXINV
> J <- 2
> R <- matrix(0:0, J, ncol(X))
> r <- matrix(0:0,J,1)
> R[1,2] <- 1
> R[2,3] <- 1
> Rbetahat <- R %*% betahat
> F <- t(Rbetahat - r) %*% solve(R %*% XTXINV %*% t(R)) %*% (Rbetahat - r) / (J * sigsq)
> F
      
           [,1]
  [1,] 23.74727
> # Compare with the lm() command (linear regression model)
> fitlm <- lm(Y ~ X[,2:ncol(X)])
> fitreslm <- lm(Y ~ X[,4:ncol(X)])
> anova(fitlm, fitreslm)
Analysis of Variance Table

Model 1: Y ~ X[, 2:ncol(X)]
Model 2: Y ~ X[, 4:ncol(X)]
  Res.Df     RSS Df Sum of Sq      F    Pr(>F)    
1     96  99.845                                  
2     98 149.241 -2   -49.397 23.747 4.178e-09 ***
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 
>