There have been concerns that women are underrepresented in Ph.D. programs in economics.In 2017, for example, "women made up 32 percent of entering PhD students in economics" (Boustan and Langan, 23).The results reported below are from the paper, "Variation in Women's Success across PhD Programs in Economics," by Leah Boustan and Andrew Langan (Journal of Economic Perspectives, 33, no. 1:Winter 2019, 2342).If you're interested, this paper freely available online, but everything you need to answer this question is provided below.

The multiple regression reported below includes a sample of 88 Ph.D. programs in economics and it reports on the share of women graduates and other department and location characteristics.

The dependent variable is the share of women graduates, measured on a zero to 1 scale, so that 0.30 in the data set means that 30 percent of the program's graduates are female. The explanatory variables are:

Rank 1120:a dummy variable equal to 1 if the department is ranked between 11 and 20, based on the U.S. News and World Report in 2017.

Rank 2130:a dummy variable equal to 1 if the department is ranked between 21 and 30, based on the U.S. News and World Report in 2017.

Rank 31+:a dummy variable equal to 1 if the department is ranked from 31 to 88, based on the U.S. News and World Report in 2017.Note that the omitted dummy variable are departments ranked in the top 10, so you can interpret the coefficient results on these variables as relative to the omitted category:departments in the top 10 in the country.The omitted category are programs ranked in the top 10.

Faculty share women:the ratio of faculty in the department who are women.For example, if one of the observations is 0.25, it means that 25 percent of the faculty are female.

Average cohort size:the average size of the entering class at each program over the past 20 years or so.

Medium city:dummy variable equal to 1 if the department is located in a city with a population more 150,000 people, but not one of the 15 largest metropolitan areas.

Large city:dummy variable equal to 1 if the department is located in one of the top 15 metropolitan areas in the United States.

The results from one of the regressions from Table 1 (p. 28) are on the following page:

Explanatory Variables:Dependent Variable: Share of Women GraduatesRank 1120: 0.035 (0.034),Rank 2130: 0.060 (0.032), Rank 31+: 0.079 (0.036),Faculty share women: 0.245 (0.130), Average cohort size: 0.000 (0.002) Medium city: 0.023 (0.019), Large city: 0.050 (0.023), Constant: 0.214 (0.056), Number of Observations: 88, R^2: 0.243

Notes:the standard errors for each coefficient are in parentheses below the coefficient.

1. Which of the estimated coefficients are statistically different from zero (ceteris paribus) at the 10percent level of significance and the 5percent level of significance?Show your work and explain.

2. Precisely interpret what the constant or intercept coefficient implies in this particular regression.Explain it in a way so that someone not familiar with multiple regression would understand it.

3. What is the predicted share of women graduates for a program in a large city, with 40 percent of the faculty women, and with an average class size of 20 students that is ranked outside of the top 30 programs?

4. What is the predicted share of women graduates for a program located outside of a large or medium city, with 10 percent of the faculty women, and with an average class size of 30 students that is ranked in the top 10 of programs nationwide?

5. Can you reject the null hypothesis at all of the coefficients (except the constant) are jointly equal to zero at the 1percent level of significance?Show your work and explain.