Question: Consider the data shown in Problem 3.26. (a) Write out the least squares normal equations for this problem and solve them for ???? and ????i,

Consider the data shown in Problem 3.26.

(a) Write out the least squares normal equations for this problem and solve them for ????̂ and ????̂i, using the usual constraint

(Σ3 i=1 ̂ ????i = 0

)

. Estimate ????1 − ????2.

(b) Solve the equations in

(a) using the constraint ̂ ????3 = 0.

Are the estimators ̂ ????i and ????̂ the same as you found in (a)? Why? Now estimate ????1 − ????2 and compare your answer with that for (a). What statement can you make about estimating contrasts in the ????i?

(c) Estimate ???? + ????1, 2????1 − ????2 − ????3, and ???? + ????1 + ????2 using the two solutions to the normal equations. Compare the results obtained in each case.

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