Task: You have some data on a sample of investment bankers, and are interested in the impacts of height and of seniority on their success. You estimate what you call Model A using a software package (which, like most econometrics packages, always reports p-values for two-sided hypothesis tests):
(A) SALARY = 90.2 + 26.7 HEIGHT_A + 13.9 SENIORITY - 52.3 PHD, Adj-R2 = 0.62
t = 2.08 t = 2.82 t = 3.1
p-value = .050 p-value = .011 p-value = 0.000
where
SALARY is measured in thousands of dollars, HEIGHT_A is adult height measured in inches and as deviations from average (using the male average for men, and the female average for women), SENIORITY is years with the employer, and PHD is a dummy equal to 1 if the person has a Ph.D.
a. How many observations do you have in your sample?
b. Your hypothesis about ADULT_HEIGHT is that positive deviations from average height raise a person’s salary, and that negative deviations from average height lowers it. Is this a one-sided or two-sided hypothesis?
c. You are not surprised that the coefficient on SENIORITY is positive. But it seems small to you, because you have recently read that “experts agree that each year of experience with an investment bank is worth another $25,000 in salary.” You have a fairly small sample, so you doubt that the difference between your estimate and that of the experts is statistically significant. But you check anyway.
What is the size of the relevant standard error for your calculation?
What is the value of the t-statistic that you compute?
What is the corresponding p-value? (If you use the table at the back of the textbook, an approximate value or a range is good enough.) ( Assume you are testing a two-sided hypothesis in this case.)
d. What salary does your model predict for a woman 70 inches tall who has been with the firm for 10 years and does not have a Ph.D.? (Assume average height for women is 65 inches)?