Last updated on May 21, 2021

Version: Spring 2018
EC200 Econometrics and Applications

Problem Set 3\

  1. The following table shows, for eight vintages of select, delicious, wine, purchases per buyer ($y$) and the wine buyer’s rating ($x$) in a given year:

    $x$ 3.6 3.3 2.8 2.6 2.7 2.9 2.0 2.6

    $y$ 24 21 22 22 18 13 9 6

    1. Estimate by hand the regression of purchases per buyer on the buyer’s rating.\

    2. Interpret the slope of the estimated regression line.\

    3. Interpret the intercept of the estimated regression line .\

  2. (Stock and Watson 4.2) Suppose that a random sample of 200 20-year-old men is selected from a population and that these men’s height and weight are recorded. A regression of weight (measured in pounds) on height (measured in inches) yields

    $$\widehat{Weight}=-99.41 + 3.94 Height$$

    $R^2 = 0.81$; $SER = 10.2$

    1. What is the predicted weight for someone who is 70 inches tall? 65 inches tall?

    2. One 20-year-old man has a late growth spurt and grows 1.5 inches over the course of the year. What is the regression’s prediction for the increase in his weight?

    3. Suppose that you want to translate the results of this equation into centimeters and kilograms. What are the regression estimates from this new regression? Give all results, including estimated coefficients, $R^2$, and SER.

    4. Interpret the $R^2$ value. Does it indicate anything about whether these estimates are likely to be biased? Explain.

  3. (Stock and Watson 5.2) Suppose tha a researcher, using wage data on 250 randomly selected male workers and 280 randomly selected female workers, estimates the following OLS regression:

    $$\begin{aligned} \widehat{Wage}=&12.52 + &2.12 Male\
    &(0.23) & (0.36)\end{aligned}$$

    $R^2 = 0.06$; $SER = 4.2$

    where $Wage$ is measured in dollars per hour and $Male$ is a binary variable equal to 1 if a person is male and 0 if female. Define the wage gender gap as the difference in mean earnings between men and women.

    1. What is the estimated gender gap?

    2. Is the estimated gender gap significantly different from zero?

    3. Construct a 95% confidence interval for the gender gap

    4. In the sample, what is mean wage of women? Of men?

    5. Another researcher uses these data, but regresses $Wage$ on $Female$, a variable equal to 1 if the person is female and 0 if the person is male. What are the regression estimates from this regression? (Include the coefficients, $R^2$, and $SER$.)

      $$\begin{aligned} \widehat{Wage}=&___ + ___ ( Female)\end{aligned}$$

      $R^2 = ___$; $SER = ___$