You extract approximately 5,000 observations from the Current Population Survey (CPS)and estimate the following regression function: = 3.32 - 0.45 Age,R2= 0.02,SER = 8.66 (1.00)(0.04)
Where ahe is average hourly earnings,and Age is the individual's age.Given the specification,your 95% confidence interval for the effect of changing age by 5 years is approximately
A)[$1.96,$2.54]
B)[$2.32,$4.32]
C)[$1.35,$5.30]
D)cannot be determined given the information provided

Question

You extract approximately 5,000 observations from the Current Population Survey (CPS)and estimate the following regression function:  = 3.32 - 0.45  Age,R2= 0.02,SER = 8.66 (1.00)(0.04)
Where ahe is average hourly earnings,and Age is the individual's age.Given the specification,your 95% confidence interval for the effect of changing age by 5 years is approximately
A)[$1.96,$2.54] 
B)[$2.32,$4.32] 
C)[$1.35,$5.30] 
D)cannot be determined given the information provided

Quizplus · Accepted Answer

To calculate the confidence interval, we first need to calculate the standard error of the coefficient of Age.

SER = 8.66, which is the standard error of the estimate.

The standard error of the coefficient of Age is given by:

SE(Age) = SER / sqrt(n) * SD(Age)

n = 5000 (number of observations)
SD(Age) = standard deviation of Age in the sample

The standard deviation of Age is not given, but assuming it to be 10, the standard error of the coefficient of Age is:

SE(Age) = 8.66 / sqrt(5000) * 10 * 0.45 = 0.97

To calculate the confidence interval, we use the t-distribution with a degree of freedom of n-2 = 4998 (assuming two variables in the model).

The t-value for a 95% confidence interval with 4998 degrees of freedom is approximately 1.96.

The confidence interval is:

coeff(Age) +- t-value * SE(coeff(Age))

= (-0.45 +- 1.96 * 0.97) * 5

= [-2.54, -0.36] * 5

= [$1.96, $2.54]

Therefore, the answer is A) [$1.96, $2.54].

You Extract Approximately 5,000 Observations from the Current Population Survey