Question

You extract 4,900 observations from the Current Population Survey (CPS) and estimate the following regression function:
$LaTeX: \begin{array}{ccccc} \widehat{\textit{ahe}} = &3.32 & - & 0.45 & \textit{Age} \\ & (1.00) & & (0.03) \end{array}$
$LaTeX: R^2 = 0.02, \textit{SER} = 8.66$
where ahe is average hourly earnings, and Age is the individual's age. Given the specification, a 95% confidence interval for the change in average ahe corresponding to an age increase of 5 years is approximately

Cannot be determined given the information provided

[-$2.54, -$1.96]

[$2.32, $4.32]

[-$1.23, $3.37]

Answer 1

from abve average change in ahe corresponding to an age increase of 5 years is $\bigtriangleup$ x=-0.45*5=-2.25

also std error of confidence interval =sqrt(SER²/n+ $\bigtriangleup$ x²*(SER*se)²)=sqrt((8.66²/4900+(2.25*0.03*8.66)²)

=0.141

hence 95% CI =estimated difference -/+ t*std error = -2.54 ; -1.96