ABSTRACT

Under the normality assumption, an unbiased estimator of o-2 can be obtained as

n

1 2

SSE —

n-— 2 —

07, 4,,,)2 (2.3.16)

1 2, v. (Y, — a — bX,)2. n-— 2 ,.,

The variance of a and b are given by

var(a) ( 1 0-2, nS ,=1 (2.3.17)

var(b) = o-2. Sxx From (2.3.17), unbiased estimators of var(a) and var(b) can be obtained simply by replacing cr2 with its unbiased estimator, o-2. This gives

var(a) = (-1 E x-,2) 6-2, nsix ‘=i (2.3.18)

,, 2 varw

1 ) = — c. Sxx Let SE(a) and SE(b) be the standard errors of a and b,

SE(a) = -\/ \(alt(a) and SE(b) = \/ (b).