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Assignment2.pdf

Economics 113

UC Santa Cruz

Summer I – 2020

Assignment 2

1. The following table contains the minimum wage and unemployment rates for a sample of six states.

a) Carefully graph unemployment and minimum wage, with unemployment on the vertical access. Draw a line that best fits the points and label the approximate intercept and slope.

b) Compute the variance of unemployment and minimum wage and compute their covariance.

c) Estimate the regression of a state’s unemployment rate on its minimum wage and write the resulting regression equation.

d) Interpret the coefficient on minimum wage in a sentence.

e) How do your estimated intercept and slope in part c) compare to your approximations in part a)?

2. Use the unemployment and minimum wage data above to answer this question.

a) What is the predicted unemployment rate for a state with a minimum wage of 10 dollars? How does this compare to the actual unemployment rate in California?

b) If a state increases its minimum wage from 10 dollars to 15 dollars, what is the predicted change in the unemployment rate?

c) Compute the predicted unemployment rate and the prediction error for each state using the regression you estimated in Question 1.

d) Compute the R-squared for your regression line. Interpret your R-squared in a sentence.

3. Use the unemployment and minimum wage data above to answer this question.

a) What assumption is required in order use regression through the origin when regressing unemployment on minimum wage? Do you think this is a reasonable assumption in this case?

Explain.

b) Compute the regression through the origin coefficients and write the resulting equation.

c) What is the predicted unemployment rate for a state with a minimum wage of 10 dollars? Compare your answer to part 2 a).

4. The following table shows wages per hour and shirts made per hour for five employees of a t-shirt factory in North Carolina.

a) What assumption is required to regress wage on shirts using regression through the origin? b) Compute the regression through the origin coefficient and write the regression equation.

c) What is the predicted wage for an employee who makes 8 shirts?

5. The following is the result of a regression of number of days sick per year on an individual’s age in years.

𝑑𝑎𝑦𝑠𝑖𝑐𝑘𝑖̂ = 4.4 + 0.08 𝑎𝑔𝑒𝑖

a) Interpret the coefficient on the person’s age in a sentence. b) What is the predicted number of days a 40 year-old is sick? c) How old would a person need to be in order for the predicted days sick to be 6.5? d) Suppose that a 30 year old is sick for 12 days. What is the regression error?

Now the regression is estimated with a binary outcome variable “eversick” that equals 0 if

the person did not get sick this year and 1 if the person did get sick this year, and with an

explanatory variable “senior” that equals 1 if the person is at least 55 years old and 0

otherwise.

𝑒𝑣𝑒𝑟𝑠𝑖𝑐𝑘𝑖̂ = 0.58 + 0.25 𝑠𝑒𝑛𝑖𝑜𝑟𝑖

e) Interpret the coefficient on “senior” in a sentence. Be precise. f) What is the likelihood that someone who is 60 years old gets sick this year?

6. The following is the result of regressing stock price on dollars of profit per share (profshare) and the number of lawsuits currently filed against the company.

𝑠𝑡𝑜𝑐𝑘𝑝𝑟𝑖𝑐𝑒𝑖̂ = 18.40 + 0.80 𝑝𝑟𝑜𝑓𝑠ℎ𝑎𝑟𝑒 − 1.70𝑙𝑎𝑤𝑠𝑢𝑖𝑡𝑠

a) Interpret the coefficient on lawsuits in a sentence.

b) What is the predicted stock price of a company with profits per share of $12.50 that currently faces three lawsuits?

c) How much higher do profits need to be in order to offset the effect of one lawsuit?

7. The following two regressions are estimated using data on the weight (in pounds) and hours of exercise per week of 2,000 people between the ages of 30 and 50.

𝑙𝑛(𝑤𝑒𝑖𝑔ℎ𝑡)𝑖̂ = 5.3 − 0.03 ℎ𝑟𝑠𝑒𝑥𝑒𝑟𝑐𝑖𝑠𝑒𝑖

𝑙𝑛(𝑤𝑒𝑖𝑔ℎ𝑡)𝑖̂ = 5.3 − 0.10 ln (ℎ𝑟𝑠𝑒𝑥𝑒𝑟𝑐𝑖𝑠𝑒𝑖 )

a) Interpret the coefficient on “hrsexercise” from the first regression in a sentence. b) If a person goes from exercising 0 hours per week to 3 hours per week, what is the predicted

change in their weight?

c) Interpret the coefficient on “ln(hrsexercise)” from the second regression in a sentence. d) If a person goes from exercising 6 hours per week to 9 hours per week, what is the predicted

change in their weight?

8. The Stata data set “gpa_college” has data on student's college GPA, high school GPA, lectures skipped during the academic year, ACT score, and other characteristics. We wish to estimate how well ACT scores predict college GPA. You must submit your do-file

(commands).

a) What is the mean and standard deviation of GPA? b) Regress college GPA on ACT score and write the estimated regression line. c) Interpret the intercept of your regression. Interpret the coefficient on ACT score in your

regression.

d) What is the predicted GPA for a student with an ACT score of 24? e) If student A has a high school GPA that is 0.2 points higher than the high school GPA of

student B, then what is the predicted difference in their ACT scores?

f) What percent of the variation in college GPA is predicted by ACT scores?

9. Using the same data, we will examine the relationship between college GPA, high school GPA, and ACT score.

a) What is the mean and standard deviation of ACT score? b) Regress college GPA on high school GPA and ACT score and write the regression line. c) Interpret the coefficient on ACT in a sentence. Interpret the coefficient on high school GPA

in a sentence. Be precise.

d) What is the predicted college GPA for a student with a 26 on the ACT and a 3.0 high school GPA?

e) Estimate the regression in part b) once just for students who never skipped a lecture. Estimate it again just for students who skipped 1 or more lectures. For which group are high school

GPA and ACT score more predictive of college GPA? Justify your answer.

f) Make a new variable that is the natural log of college GPA and a new variable that is the natural log of ACT score. Regress the natural log of college GPA on the natural log of ACT score and write the resulting regression equation. Interpret the coefficient on the natural log

of ACT in a sentence.