xy = read.table('data020101.txt')

y = xy$V1
x1 = xy$V2
x2 = xy$V3
x3 = xy$V4

reg = lm(y~x1+x2+x3)

summary(reg)

xnew = data.frame(x1 = c(50), x2 = c(50), x3 = 2)

pred = predict(reg, xnew, interval="confidence", level=0.95)

pred

# after removing X2, we fit the simplified model

reg1 = lm(y~x1+x3)

summary(reg1)

pred1 = predict(reg1, xnew, interval="confidence", level=0.95)

pred1