Question

WAGE = B1 B2EDUC+B3Exper + BExper + e, using a random sample of 54 observations. The least square estimates and the corresponding estimated covariance matrix are given by b1 -13 -0.2 -0.125 0.01 2.5 -0.2 0.16 0.01 0 b2 Var(b) = 0.5 -0.125 0.01 0.04 0.12 b4 0.01 -0.01 0.12 0.09 29. The 95% confidence interval for B4 is (a) -0.813,0.793] 12 (b) -0.731,0.711] (c) [-0.613, 0.593] [CORRECT ANSWER] (d) 0.513,0.493|] (e) [-0.216, 0.193]

Answer 1

The confidence interval is given by the following formula

B- to.025,52 * SD(B), Bto.025,52* SD()]

Here, total number of observations = 54. So, we have degrees of freedom = 52

From the tables, we have the t value for 52 degrees of freedom as

t(0.025,52)=2.007

Also, we have from the given information the following values

BA -0.01

Var(40.09

. SD(84) = V0.09 0.3

So, the confidence interval is:

0.01 (2.007) (0.3),-0.01(2.007) (0.3)]

-0.6121,0.5921

The answer is closest to Option (c). Thus, the confidence interval is

(c) [-0.613, 0.593]