pdf("rpd4_9r.pdf")


alldata <- matrix( 
c(44,89.47,44.609,11.37,62,178,182,
40,75.07,45.313,10.07,62,185,185,
44,85.84,54.297,8.65,45,156,184,
42,68.15,59.571,8.17,40,166,172,
38,89.02,49.874,9.22,55,178,180,
47,77.45,44.811,11.63,58,176,176,
40,75.98,45.681,11.95,70,176,180,
43,81.19,49.091,10.85,64,162,170,
44,81.42,39.442,13.08,63,174,176,
38,81.87,60.055,8.63,48,170,186,
44,73.03,50.541,10.13,45,168,168,
45,87.66,37.388,14.03,56,186,192,
45,66.45,44.754,11.12,51,176,176,
47,79.15,47.273,10.6,47,162,164,
54,83.12,51.855,10.33,50,166,170,
49,81.42,49.156,8.95,44,180,185,
51,69.63,40.836,10.95,57,168,172,
51,77.91,46.672,10,48,162,168,
48,91.63,46.774,10.25,48,162,164,
49,73.37,50.388,10.08,67,168,168,
57,73.37,39.407,12.63,58,174,176,
54,79.38,46.08,11.17,62,156,176,
52,76.32,45.441,9.63,48,164,166,
50,70.87,54.625,8.92,48,146,186,
51,67.25,45.118,11.08,48,172,172,
54,91.63,39.203,12.88,44,168,172,
51,73.71,45.79,10.47,59,186,188,
57,59.08,50.545,9.93,49,148,160,
49,76.32,48.673,9.4,56,186,188,
48,61.24,47.92,11.5,52,170,176,
52,82.78,47.467,10.5,53,170,172),byrow=T,ncol=7)

Y <- alldata[,3]
X <- alldata[,4:7]

XF <- cbind(rep(1,nrow(X)),X)

XPXINVF <- solve(t(XF) %*% XF)
BETAHATF <- XPXINVF %*% t(XF) %*% Y

ix <- diag(1,ncol=nrow(X),nrow=nrow(X))
jx <- matrix(rep(1,nrow(X)*nrow(X)),ncol=nrow(X)) 

SSRESIDF <- t(Y) %*% (ix - XF %*% XPXINVF %*% t(XF)) %*% Y
DFRESIDF <- nrow(XF)-ncol(XF)

XR1 <- cbind(rep(1,nrow(X)),X[,1],X[,3])

XPXINVR1 <- solve(t(XR1) %*% XR1)
BETAHATR1 <- XPXINVR1 %*% t(XR1) %*% Y

SSRESIDR1 <- t(Y) %*% (ix - XR1 %*% XPXINVR1 %*% t(XR1)) %*% Y
DFRESIDR1 <- nrow(XR1)-ncol(XR1)

Q1 <- SSRESIDR1-SSRESIDF

SSRESIDF
SSRESIDR1
Q1

Y2 <- Y-rep(90,nrow(Y))

XR2 <- cbind(X[,1],X[,3])

XPXINVR2 <- solve(t(XR2) %*% XR2)
BETAHATR2 <- XPXINVR2 %*% t(XR2) %*% Y2

SSRESIDR2 <- t(Y2) %*% (ix - XR2 %*% XPXINVR2 %*% t(XR2)) %*% Y2
DFRESIDR2 <- nrow(XR2)-ncol(XR2)

Q2 <- SSRESIDR2-SSRESIDF

SSRESIDF
SSRESIDR2
Q2

dev.off()