Statistics - Regression Projects

Suppose you are interested in whether MBAs work more hours per week than people with other graduate degrees.

Suppose you are interested in whether MBAs work more hours per week than people with other graduate degrees. You have an independent random sample of people in the US with graduate degrees that has information on the hours worked per week in 2000 (Hours), whether they have an MBA (MBA=1 if they do, 0 if not), a gender indicator (Gender =1 if female, 0 if not), and an indicator for whether they have a Prestigious MBA or not (Pres MBA=1 if they do, 0 if not). Further suppose you started with the following regression:

\[Hour{{s}_{i}}=a+b\,Gende{{r}_{i}}+c\,MB{{A}_{i}}+f\,(Gende{{r}_{i}}*MB{{A}_{i}})+{{\varepsilon }_{i}}\]

Your OLS estimates are:

Parameter Point Est. Std. Error

a 36 3.5

b -1.1 .4

c 8.0 2.1

f 2.7 1.2

Does this regression provide evidence that the average hours worked by women is less than the average hours worked for men? Explain.
Suppose that you wanted to add additional terms to this regression equation (Without removing terms) using your variables described above to test whether the average hour worked per week among women with a prestigious MBA is the same as the average hours per week worked by men with a prestigious MBA. Exactly what regression would you run and what hypothesis would you want to test? Write down regression equation(s), label coefficients, and write out the hypothesis you want to test in terms of your model’s parameters.

2. Suppose you are interested in understanding Coca-Cola profits as a function of temperature, and city-wide promotion data. You have data on Coke profits (sales - costs) in ($1000s) from 300 cities for the month of June 1993, average temperature for that month in degrees Fahrenheit, a variable that is the number of days that month when there were half-page newspaper ads for Coke, and a dummy variable equal to one if the city is in the Southeastern US. You have estimated the following regression:

\[profi{{t}_{i}}=a+b\,s{{d}_{i}}+c\,{{F}_{i}}+d\,F_{i}^{2}+f\,Days{{ & }_{i}}+{{\varepsilon }_{i}}\]

Your OLS estimates are:

Parameter Point Est. Std. Error

a -230 35

b 2000 600

c 10 4

d .0008 .002

f 5 1.5

Does there appear to be a statistically significant increasing marginal effect of temperature on Coke profits?
Does the intercept estimate and standard error indicate that Coke is losing money in the northern US?
How would you add terms to this regression to allow the marginal effect of temperature to be different in the Southeast US from the rest of the country?
If each ad day costs $500 what is probably the expected profit maximizing number of ad days?

3. Guy is interested in the determinants of growth in emerging markets, in particular whether education (human capital), political stability, and fiscal variables play a role. He has run the following regression of growth rates for countries from 1960 to 1985 upon country characteristics. The average annual growth rate of real (inflation-adjusted) GDP per capita from 1960 to 1985 (2% growth is .02) is regressed on: a constant, initial values of real GDP(GDP60) per capita (in $1000s), secondary and primary school enrollment rates in fractions (SEC60 and PRIM60), the share of real government ‘consumption’ expenditures to real GDP for 1970-1985 ( ${{g}^{c}}/y$ ), revolutions from 1960-1985 (REV), assassinations per million (ASSASS), and region indicator variables for Africa and Latin America. Guy got the following estimates (the dependent variable is Growth Rate of Real GDP 1960-85). Is this evidence consistent with the following claims made by Guy, or not? Explanation required.

There does not seem to be any relationship between political unrest and growth.
If all I know about a country is that it is in Latin America, I should expect that
its growth rate is less than the average growth rate for non-African, non-Latin American countries.
If there were two groups of countries, A and B, that are identical in terms of all
these regressors except that countries in group A have a government consumption to output ratio ${{g}^{c}}/y$ that is twice the ${{g}^{c}}/y$ of the countries in group B; then on average, group A countries grew approximately 5% to 15% faster than those in B.
The difference between average growth for two groups of countries that were identical except one had a primary school enrollment rate of .80 and one had an enrollment rate of .90 is probably more than one percentage point.

4. Use the data on executive compensation from Compustat in the worksheet execs.xls from the course webpage for this question. This dataset contains data on 2001 compensation for 3595 top executives for a large set of publicly traded firms. It also contains data on each person’s gender, age, job title and their company’s market value.

Run a regression of salary on the gender indicator and report point estimates,
standard errors, and R-squared. Do men and women executives have different
salaries? Does gender explain a large portion of the variation in executives’ salary?
Run a regression of salary on the gender indicator, age, and market value of the firm. Do men and women executives still appear to have different salaries controlling for these firm and individual characteristics?
The column labeled "Job Title" contains a description of the job title held by each of the executives in the sample. Using your best judgment, define 3 or more groups of people that you think have similar job responsibilities, each with at least 30 members. Choose one group to be the base and create 2 or more indicator variables for membership in the remaining groups. Add these 2 or more group indicators to the salary regression along with the gender indicator, age, and market value of the firm. For example, suppose your groups were: anyone with the words "vice president" in their job title, anyone whose title included "CEO", and all other jobs. You could then use "vice presidents" as the base group and define an indicator for being in the "CEO" group and another indicator for being in the "Other Job" group. Your regression would then be of salary on a constant, "CEO" indicator, "Other Job" indicator, the gender indicator, age, and market value of the firm. Report your group definitions as well as the point estimates and standard errors and R-squared from this regression. What does this regression tell you about the difference in executive salaries for men versus women?
Now replicate part (c) using Total 2001 Compensation as the dependent variable. This measure of total compensation includes salary, bonus, and value of options granted in 2001. Report point estimates, standard errors, and R-square from a regression of total compensation upon a gender indicator, age, firm market value, and your job category indicators. Are your conclusions about gender differences in executives’ earnings altered by using this more inclusive measure of compensation?

5. Use the census wage data for 1990 for this question. The last column in this spreadsheet is wage and salary income for the year, which can equal to zero (e.g. for the self-employed). For this question, use only those individuals with nonzero wage and salary income. Create a weekly "wage" by dividing total wage and salary income by weeks worked and call it W.

Run an OLS regression of W on a constant, a male/female indicator, age, and age squared to estimate quadratic age-profiles for men and women that are the same shape except for a vertical shift. Plot the profiles implied by your point estimates over the range of 18 to 65 years of age on the same graph. What is a point estimate for the age at which the profiles peak?

Price: $34.6

Solution: The downloadable solution consists of 13 pages, 2160 words and 8 charts.
Deliverable: Word Document