# Question

Show that

(a) ∑2, the random variable corresponding to 2, is not an unbiased estimator of σ2;

(b) S2e = n·∑2 / n–2 is an unbiased estimator of σ2. The quantity se is often referred to as the standard error of estimate.

(a) ∑2, the random variable corresponding to 2, is not an unbiased estimator of σ2;

(b) S2e = n·∑2 / n–2 is an unbiased estimator of σ2. The quantity se is often referred to as the standard error of estimate.

## Answer to relevant Questions

Using se (see Exercise 14.18) instead of , rewrite (a) The expression for t in Theorem 14.4; (b) The confidence interval formula of Theorem 14.5. Exercise 14.18 Show that (a) ∑2, the random variable corresponding to ...Use the results of Exercises 14.20 and 14.21 and the fact that E(Bˆ) = β and var(Bˆ) = σ2/ Sxx to show that Yˆ0 = Aˆ + Bˆ is a random variable having a normal distribution with the mean And the variance Also, use the ...Use the formula for t of Exercise 14.28 to show that if the assumptions underlying normal regression analysis are met and β = 0, then R2 has a beta distribution with the mean 1 / n – 1. In exercise With x01, x02, . . . , x0k and X0 as defined in Exercise 14.39 and Y0 being a random variable that has a normal distribution with the mean β0 + β1x01 + · · · + βkx0k and the variance σ2, it can be shown that Is a ...If a set of paired data gives the indication that the regression equation is of the form µY|x = α ∙ βx, it is customary to estimate a and β by fitting the line to the points {(xi, logyi); i = 1, 2, . . . , n} by the ...Post your question

0