Econ B2000, MA Econometrics

Kevin R Foster, the Colin Powell School at the City College of New York, CUNY

October 22, 2019

The questions are worth 120 points. You have 120 minutes to do the exam, one point per minute.
All answers should submitted electronically. Please submit all relevant computer files. Please no “pages” files, save as pdf or rtf. I prefer .Rmd files. No need to put your name, just last digits of ID to identify yourself, so grading is blind. You may refer to your books, notes, calculator, computer, or astrology table. The exam is “open book.” However, you must not refer to anyone else, either in person or electronically, during the exam time. For instance, since these exam questions are newly created, posting questions or copying answers on online homework helping sites or forums (such as Chegg, Yahoo answers or others) is a violation. You must do all work on your own. Cheating is harshly penalized. Please silence all electronic noisemakers such as mobile phones. Good luck. Stay cool.

  1. (20 points) Please answer the following; you might find it useful to make a sketch.
  1. For a Normal Distribution that has mean -6 and standard deviation 9.8 , what is the area to the left of -19.72 ?
  2. For a Normal Distribution that has mean 9 and standard deviation 4.6 , what is the area in both tails farther from the mean than -0.66 ?
  3. For a Normal Distribution that has mean -8 and standard deviation 7.3 , what is the area to the right of -19.68 ?
  4. For a Normal Distribution that has mean -12 and standard deviation 9.4 , what is the area to the right of 10.56 ?
  5. For a Normal Distribution that has mean 2 and standard deviation 0.4 , what is the area to the left of 2.36 ?
  6. For a Normal Distribution that has mean 4 and standard deviation 2.2 , what is the area to the right of 2.9 ?
  7. For a Normal Distribution that has mean -4 and standard deviation 1.4 , what is the area in both tails farther from the mean than -5.68 ?
  8. For a Normal Distribution that has mean 1 and standard deviation 9.8 , what is the area in both tails farther from the mean than -22.52 ?
  9. For a Normal Distribution that has mean -12 and standard deviation 4.6 what two values leave probability 0.441 in both tails?
  10. For a Normal Distribution that has mean -11 and standard deviation 8.4 what two values leave probability 0.248 in both tails?
  11. A regression coefficient is estimated to be equal to 7.02 with standard error 5.4 ; there are 17 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero?
  12. A regression coefficient is estimated to be equal to 4.96 with standard error 6.2 ; there are 6 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero?
  13. A regression coefficient is estimated to be equal to -9.2 with standard error 4.6 ; there are 18 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero?
  1. (20 points) In a regression trying to explain student grades in Intermediate Macro class (grades are represented as a number from 4, which is an A, down to 0 for F), we use grades in 4 prerequisite classes: calculus, Eco 101, Eco 102, and Eco 103. Consider this output:
Estimate Std. Error
(Intercept) 0.93155 0.23881
GP.Calc 0.11545 0.03034
GP.Eco101 0.19374 0.06487
GP.Eco102 0.32428 0.05108
GP.Eco103 -0.01309 0.05428
  1. What is the t-statistic and p-value for each estimated coefficient?
  2. Discuss which variables are statistically significant. Are there surprises? Explain. What available data might improve the predictive power of this regression?

  1. (20 points) In the PUMS NY data that we’ve been using in class, those with TRANWORK == 70 are working from home. Compare that group of people with those commuting on the subway (there’s a dummy Commute_subway or use TRANWORK == 33). What are the educational attainments in each group? Given that someone works from home, what is the likelihood that the person has at least a 4-year degree? Given that someone is female, what is the likelihood that she works at home? Given that someone is male, what is the likelihood that he works at home? Create a confidence interval for the difference and provide a p-value.

  2. (40 points) With the same data, create a different regression where TRANTIME is the dependent variable (you can drop the ones with zero values). What is the effect (if any) of educational qualification on commuting time? What about other demographic effects such as age and race/ethnicity? Explain confidence intervals and p-values for each important coefficient (where your explanation determines important). Create a joint hypothesis test to find a p-value for whether all of the education dummies are all equal to zero. Calculate predicted values for some people and assess if these seem plausible. Perhaps a graph of data and predicted values.

  3. (20 points) Create a k-nn model to try to predict how a person commutes to work. (Worry a bit about the zero values of TRANWORK since that typically means they’re not working.) How useful is this model at predicting? What are some of the important variables in this prediction?