Confidence Interval #2

Confidence Interval #2
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Let Y = Xβ + ε,where ε N ( 0,σ2IN),and
β is a p-dimensional vector,with N=10 and p=3.
Given y'y = 58,and given the following normal equations.
4β1(hat) + 2β2(hat) - 2β3(hat) = 4
2β1(hat) + 2β2(hat) + β3(hat) = 7
-2β1(hat) + β2(hat) +6β3(hat) = 9
a.Find the least squares estimates of β and σ2.
b.What are the estimates of β1,β2,β3,β1-β2,and β1+β3?
c.Assume that the errors have a normal distribution.
Construct 95% confidence intervals for β1,β2,β3,β1-β2,and β1+β3.
Reference:
Title:A First Course in Linear Model Theory
Author:Nalim Ravishankar & Dipak K.Dey
Publisher:Chapman & Hall / CRC
ISBN:9781584882476