Problem Set 6

Problem Set 7

Textbook problems:
6.8 (a), (b), 6.11 (a), (b), (d)

Computer exercises:

1. Go back to the computer excercise in problems set 6. Are your estimated coefficients statistically significant? How does considering statistical significance (testing whether B1=0 and B2=0) change your conclusions?

2. The dataset cities.txt or cities.dta contains information about 60 cities in the U.S. for following variables:

city - Name of City/Metro Area
pop1993 - 1993 Population (000)
rshctrs - Number of Research Centers
ba - percentage of pop. with BA or + Degrees of 25 yrs +
grad - percentage of pop. with Grad Degree of 25 yrs +
patents - Patents Issued 1988-92
innov - Rank: Presence Innovative Firms
probiz - Rank: Pro-Business Attitude
patcap - Patents per 1,000 Population
ctrcap - Research Centers per 1,000 Pop

(a) Estimate a simple regression model with patents per capita as the dependent and the percentage of graduate degrees as the independent variables. How do you interpret your estimated coefficients?

(b) Can you confidently conclude from these results that having a more educated population (that is, a higher percentage of people with graduate degrees) leads to more inventive activity in a city? Suggest reasons why you might think otherwise.

3. The dataset husbands.txt or husbands.dta contains information on 199 married couples and has the following variables:

ageh - Husband's age
heighth - Height of Husband
agew - Age of Wife
heightw - Height of Wife
agehm - Age of husband at marriage

(a) Test the following hypothesis: "The height of an individual does not tell you anything about the height of his/her spouse."

(b) Suppose we hypothesize that, on average in the population, an increase of one inch in the height of a woman is associated with an increase of 0.5 inches in the height of her husband. Test this hypothesis against the alternative that an increase of one inch in the height of a woman is associated with an increase of more than 0.5 inches in the height of her husband.