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# PS3.4 for Example 3.8 on conf. intervals
open data3-1
ols 1 0 2
# generate predicted price
genr phat = price - $uhat
# retrieve the number of obs.
genr n = $nobs
# retrieve degrees of freedom
genr df = $df
# retrieve sigma squared
genr sgmasq=$ess/df
# get mean of sqft
genr xbar=mean(sqft)
# get s.d. of sqft
genr sdx = sd(sqft)
# reset sample range
smpl 1 1
# calculate sxx
genr sxx = 13*sdx*sdx
# other variables for confidence interval calculation
genr x0 = 2000
genr temp1=((x0-xbar)^2)/sxx
genr temp2=(temp1+(1/n))
# calculate using equations 3.28 and 3.29
genr sysq1=sgmasq*temp2
genr sysq2=sgmasq*(1+temp2)
# take square root for standard errors
genr sy1=sqrt(sysq1)
genr sy2=sqrt(sysq2)
# predict mean y for x0
genr ymean0=52.351+(0.13875*x0)
# compute bounds for confidence interval using equation 3.28
genr ymean1=ymean0-(2.179*sy1)
genr ymean2=ymean0+(2.179*sy1)
# compute bounds for confidence interval using equation 3.29
genr y1=ymean0-(2.179*sy2)
genr y2=ymean0+(2.179*sy2)
# compute large sample confidence interval, that is, plus/minus 2 sigma
genr sgmahat = sqrt(sgmasq)
genr y3 = ymean0 - (2*sgmahat)
genr y4 = ymean0 + (2*sgmahat)
print -o n df sgmasq xbar sdx sxx sysq1 sysq2 sy1 sy2 ymean0 ymean1 \
ymean2 y1 y2 y3 y4
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