Use the cig_1st_diff data set. This is based on the changes from 1990 to 2000 , and it is extracted from the data set used in Question #3. Estimate a first-difference model, as follows: regress cigch on taxch, uratech, and beertaxch. Weight the model by pop 2000 , and use robust standard errors. Interpret the estimate on taxch.

From the example in Section 8.5 from Card and Krueger (1994) on estimating the effects of minimum-wage increases on employment, write out the regression equation for the difference-in-difference model.

Use the data set oecd_gas_demand. From Question #7 in Chapter 3, add fixed effects for the country, along with a heteroskedasticity correction.
a. How does the coefficient estimate on lrpmg change from Question #7 in Chapter 3 with the fixed effects added?
b. How does this change which observations are compared to which observations?

Return to the tv-bmi-ecls data set used for Exercise $# 5$ in Chapter 6 . From that exercise, along with other descriptions of the research issue, there is much potential omitted-factors bias.
a. Explore the data description and variable list (from the file “Exercises data set descriptions” on the book’s website). Design a model to address the omitted-factors bias.
b. Are there any shortcomings to your approach?

1. Indicate which of the four main regression objectives each of the following research issues would be:
   a. What 4th-grade teacher did best given his/her students’ prior achievement?
   b. What is the best guess for how many sailors the Navy will recruit this year?
   c. Do people who swear have higher intelligence?
   d. How much does keeping up with the material affect your eventual grade in the class?
   e. Does keeping up with the material affect your eventual grade in the class?

2. Suppose that, in a particular city, a regression of prices of homes sold in the prior year (price) on the number of bedrooms (bedrooms) and square feet (sqft) yields the following regression model:
   $$
   \widehat{\text { price }}=100,000+45,000 \times \text { bedrooms }+10 \times \text { sqft }
   $$
   a. Interpret the coefficient estimate on sqfi.
   b. If a home had 2 bedrooms and was 1500 square feet, what would the predicted price be?
   c. If that home had a selling price of $\$ 170,000$, what would be the residual?
   d. How would you interpret the residual?
   e. What is a possible reason for the residual being what it is?

3. From the book’s website, use the data set, democracy2. This is a data set of observations by country and year, with measures of democracy, life expectancy, and several other factors and outcomes. (see https://www.v-dem.net/). Use 1985 observations with condition1=1 (which is that there are non-missing values for all variables used in this regression).
a. Calculate the means and standard deviations of the following four variables to get a sense of the scales of the variable:

• life_exp (life expectancy)
• democracy (an index of the level of democracy in a county on a 0-1 scale)
• augeduc (average years of education)
• educgini (inequality Gini coefficient for years of education, on a 0-100 scale).
  b. Regress life_exp on democracy, avgeduc, and educgini. Interpret the coefficient estimate on democracy.
  c. For a country with life-exp $=60$, democracy $=0.5$, avgeduc $=10$, and educgini $=50$, what is the predicted value of the dependent variable and the residual?
  d. Interpret the predicted value and the residual.
  e. Interpret the $R^2$.
  f. Add urbanpct (the percent of the population living in an urban area) as an explanatory variable to the model. Interpret the change in $R^2$ after adding urbanpct.

4. From the book’s website, use the data set, income. Estimate three separate models, with income as the dependent variable. Include just one of the three explanatory variables (educ, afqt, age) in each model. Which explanatory variable explains the greatest amount of variation in income? How did you arrive at your answer?