Practice for Exam 2

Econ B2000, MA Econometrics

Kevin R Foster, CCNY

Fall 2012

Not all of these questions are strictly relevant; some might require a bit of knowledge that we haven't covered this year, but they're a generally good guide.

1. You might find it useful to make a sketch.

a. For a Normal Distribution with mean 1 and standard deviation 1.7, what is area in both tails farther from the mean than 1.9? A. 0.4013 B. 0.6915 C. 0.2630 D. 0.6171

b. For a Normal Distribution with mean 3 and standard deviation 4.7, what is area in both tails farther from the mean than -0.3? A. 0.7384 B. 0.9679 C. 0.2616 D. 0.4839

c. For a Normal Distribution with mean -7 and standard deviation 8.1, what is area in both tails farther from the mean than -17.5? A. 0. 2551 B. 0.1936 C. 0.7422 D. 0.3872

d. For a Normal Distribution with mean -4 and standard deviation 5.7, what is area in both tails farther from the mean than -16.0? A. 0.9821 B. 0.1587 C. 0.7586 D. 0.0357

e. For a Normal Distribution with mean -11 and standard deviation 5.7, what is area in both tails farther from the mean than -12.1? A. 0.5398 B. 0.8415 C. 0.5793 D. 0.9732

f. For a Normal Distribution with mean -10 and standard deviation 8.3, what is area in both tails farther from the mean than -8.3? A. 0.1141 B. 0.5793 C. 0.8859 D. 0.8415

g. For a Normal Distribution with mean 11 and standard deviation 0.8, what is area in both tails farther from the mean than 10.6? A. 0.4314 B. 0.1587 C. 0.6171 D. 0.5987

h. For a Normal Distribution with mean -3 and standard deviation 0.8, what is area in both tails farther from the mean than -4.0? A. 0.7422 B. 0.9032 C. 0.0001 D. 0.1936

i. For a Normal Distribution with mean -3 and standard deviation 1.0, what is area in both tails farther from the mean than -4.8? A. 0.9641 B. 0.1437 C. 0.8159 D. 0.0719

j. For a Normal Distribution with mean -15 and standard deviation 0.4, what is area in both tails farther from the mean than -15.7? A. 0.7317 B. 0.1783 C. 0.0891 D. 0.8023

k. For a Normal Distribution with mean 8 and standard deviation 0.8, what is area in both tails farther from the mean than 9.7? A. 0.7757 B. 0.1587 C. 0.1469 D. 0.0357

l. For a Normal Distribution with mean 1 and standard deviation 3.5, what values leave probability 0.469 in both tails? A. (-1.5344 3.5344) B. (0.7278 1.2722) C. (6.3837 -4.3837) D. (-0.4384 1.0098)

m. For a Normal Distribution with mean -8 and standard deviation 1.7, what values leave probability 0.114 in both tails? A. (-8.0494 -5.9506) B. (-10.6868 -5.3132) C. (-9.2673 -6.7327) D. (-6.2863 -3.1254)

n. For a Normal Distribution with mean -9 and standard deviation 9.0, what values leave probability 0.489 in both tails? A. (-9.2482 -8.7518) B. (-15.2271 -2.7729) C. (-0.6919 0.6919) D. (9.1268 -27.1268)

o. For a Normal Distribution with mean 3 and standard deviation 2.6, what values leave probability 0.301 in both tails? A. (1.6554 4.3446) B. (0.3108 5.6892) C. (3.6722 2.3278) D. (-1.0343 1.0343)

p. For a Normal Distribution with mean -5 and standard deviation 4.2, what values leave probability 0.254 in both tails? A. (-9.7909 -0.2091) B. (-1.1407 1.1407) C. (-4.9158 -5.0842) D. (-7.3954 -2.6046)

q. For a Normal Distribution with mean 13 and standard deviation 7.3, what values leave probability 0.244 in both tails? A. (-2.0048 15.0048) B. (12.7804 13.2196) C. (7.9375 18.0625) D. (4.4952 21.5048)

r. For a Normal Distribution with mean 1 and standard deviation 5.2, what values leave probability 0.116 in both tails? A. (-5.2152 7.2152) B. (-7.1733 9.1733) C. (-7.6733 8.6733) D. (-3.0866 5.0866)

s. For a Normal Distribution with mean -4 and standard deviation 9.9, what values leave probability 0.020 in both tails? A. (-2.3263 2.3263) B. (-21.3318 13.3318) C. (-27.0308 19.0308) D. (-24.3321 16.3321)

t. For a Normal Distribution with mean -11 and standard deviation 7.2, what values leave probability 0.054 in both tails? A. (-19.3732 8.3732) B. (-22.5722 0.5722) C. (-24.8732 2.8732) D. (-17.9366 -4.0634)

u. For a Normal Distribution with mean 12 and standard deviation 8.9, what values leave probability 0.167 in both tails? A. (5.8505 18.1495) B. (8.1828 15.8172) C. (-0.2990 24.2990) D. (-1.3819 1.3819)

v. For a Normal Distribution with mean 12 and standard deviation 0.3, what values leave probability 0.245 in both tails? A. (11.9925 12.0075) B. (38.8374 41.1626) C. (11.6512 12.3488) D. (14.8256 18.1744)

2. You might find it useful to make a sketch.

a. A regression coefficient is estimated to be equal to -5.968 with standard error 4.7; there are 4 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 1.7958 B. 0.5540 C. 0.2730 D. 0.7270

b. A regression coefficient is estimated to be equal to -9.880 with standard error 9.7; there are 21 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.6830 B. 0.3200 C. 0.8694 D. 0.6500

c. A regression coefficient is estimated to be equal to -10.781 with standard error 6.6; there are 20 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.1180 B. 0.0003 C. 0.2390 D. 0.9700

d. A regression coefficient is estimated to be equal to 4.456 with standard error 4.9; there are 12 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.0060 B. 0.2346 C. 0.6190 D. 0.3810

e. A regression coefficient is estimated to be equal to 6.696 with standard error 4.2; there are 31 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.1210 B. 1.8891 C. 0.8790 D. 0.6609

f. A regression coefficient is estimated to be equal to 32.530 with standard error 10.0; there are 7 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.9860 B. 0.0140 C. 0.0017 D. 0.6991

g. A regression coefficient is estimated to be equal to -6.463 with standard error 4.8; there are 5 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.0089 B. 1.8218 C. 0.2360 D. 0.8581

h. A regression coefficient is estimated to be equal to 7.335 with standard error 3.4; there are 19 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.5060 B. 0.0440 C. 0.9560 D. 0.1750

i. A regression coefficient is estimated to be equal to -6.564 with standard error 3.1; there are 7 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.0720 B. 0.9239 C. 0.9280 D. 0.1386

j. A regression coefficient is estimated to be equal to -8.619 with standard error 6.1; there are 25 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.1493 B. 0.1700 C. 0.9500 D. 0.8300

k. A regression coefficient is estimated to be equal to 7.966 with standard error 8.8; there are 17 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.3780 B. 0.6347 C. 0.8510 D. 0.2575

l. A regression coefficient is estimated to be equal to 10.254 with standard error 6.7; there are 26 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.1380 B. 0.8620 C. 0.0965 D. 0.9352

m. A regression coefficient has standard error 4.60; there are 14 degrees of freedom. The t-statistic is 1.3942. What is the coefficient? A. 0.1376 B. 0.3357 C. 6.4132 D. 0.4581

n. A regression coefficient has standard error 4.70; there are 6 degrees of freedom. The t-statistic is 1.7159. What is the coefficient? A. 0.3849 B. 6.8630 C. 8.0647 D. 1.9138

o. A regression coefficient has standard error 4.30; there are 21 degrees of freedom. The t-statistic is 1.1602. What is the coefficient? A. 0.3331 B. 4.9887 C. 8.7410 D. 0.1866

p. A regression coefficient has standard error 6.60; there are 24 degrees of freedom. The t-statistic is 1.5223. What is the coefficient? A. 1.8721 B. 0.4186 C. 10.0472 D. 7.8590

q. A regression coefficient has standard error 5.40; there are 27 degrees of freedom. The t-statistic is -1.6674. What is the coefficient? A. -9.0038 B. 0.0954 C. 0.8930 D. 1.0433

r. A regression coefficient has standard error 1.10; there are 5 degrees of freedom. The t-statistic is -3.1285. What is the coefficient? A. -3.4414 B. -2.0018 C. 0.9740 D. 0.6120

s. A regression coefficient is estimated to be equal to 16.483; there are 10 degrees of freedom. The t-statistic is 2.7937. What is the standard error? A. 0.0102 B. 5.9000 C. 46.0716 D. 1.6483

t. A regression coefficient is estimated to be equal to -2.806; there are 8 degrees of freedom. The t-statistic is -1.0394. What is the standard error? A. 0.2986 B. 0.7436 C. -0.3508 D. 2.7000

u. A regression coefficient is estimated to be equal to -11.059; there are 11 degrees of freedom. The t-statistic is -1.1641. What is the standard error? A. 12.9570 B. -1.0054 C. 9.5000 D. 0.8512

v. A regression coefficient is estimated to be equal to 13.066; there are 25 degrees of freedom. The t-statistic is 1.5743. What is the standard error? A. 8.3000 B. 20.5795 C. 1.8846 D. 0.0831

w. A regression coefficient is estimated to be equal to 15.167; there are 6 degrees of freedom. The t-statistic is 3.0333. What is the standard error? A. 5.0000 B. 0.9770 C. 0.0076 D. 1.9976

x. A regression coefficient is estimated to be equal to 6.136; there are 28 degrees of freedom. The t-statistic is 1.2271. What is the standard error? A. 0.2191 B. 0.7700 C. 5.0000 D. 7.6024

Subsequent questions will use the BRFSS dataset (I know, all the variable labels are ALL CAPS like some elderly aol user typed them, sorry), the Behavioral Risk Factor Surveillance Study. There are many observations on a wide variety of risky behaviors: smoking, drinking, poor eating, flu shots, whether household has a 3-day supply of food and water... I put a dataset for the exam on Blackboard.

For now concentrate on BMI, which is Body Mass Index, a measure of whether a person is overweight (2500-2999) or obese (3000 or above). Note there are 2 implied decimals so that 2490 is 24.90, the upper limit for 'normal weight'. And note that values of 9999 are missing so make sure to omit those.

3. What are descriptive statistics for BMI? Does this suggest some way you ought to limit the sample? Construct a hypothesis test for whether there is no statistically significant difference between men and women (you can limit to specific ages or by other variables if you wish). What is the standard error of the difference? What is the test statistic? What is the p-value? What is the chance of selecting a female who is underweight (BMI<1850)? What is the chance of selecting a male who is underweight? What is the chance of selecting a person who is underweight, of the females (i.e. conditional on being female)? What is the chance of selecting a person who is underweight, of the males?

4. What explanatory variables could be in the model? Which are available in the BRFSS data? Construct at least one simple regression model; discuss the estimates (including statistical significance but also relevance and whether the estimates accord with theory). Should income be in the model? Explain whether income and BMI might be endogenous.

5. Construct another reqression model with more complicated interactions. How could you improve the model? Consider nonlinear age terms, gender-age interactions, race-age interactions, state dummies and more. Note that INCOME2 is not a continuous variable but you would need to create dummy variables for the relevant income levels.

6. You might find it useful to sketch the distributions.

a. For a Normal Distribution with mean 1 and standard deviation 9.6, what is area in both tails farther from the mean than 23.1? A. 0.1251 B. 0.0214 C. 0.4585 D. 0.9893

b. For a Normal Distribution with mean 5 and standard deviation 7.6, what is area in both tails farther from the mean than 14.1? A. 0.2743 B. 0.1587 C. 0.2301 D. 0.4603

c. For a Normal Distribution with mean -2 and standard deviation 3.8, what is area in both tails farther from the mean than 2.9? A. 0.7007 B. 0.1936 C. 0.3872 D. 0.2578

d. For a Normal Distribution with mean -7 and standard deviation 5.1, what is area in both tails farther from the mean than -1.9? A. 0.3173 B. 0.0849 C. 0.6346 D. 0.9151

e. For a Normal Distribution with mean 13 and standard deviation 3.5, what is area in both tails farther from the mean than 7.8? A. 0.2672 B. 0.1336 C. 0.1587 D. 0.7734

f. For a Normal Distribution with mean -12 and standard deviation 9.6, what values leave probability 0.003 in both tails? A. (-2.9677, 2.9677) B. (-38.3787, 14.3787) C. (-36.1166, 12.1166) D. (-40.4903, 16.4903)

g. For a Normal Distribution with mean -2 and standard deviation 9.1, what values leave probability 0.092 in both tails? A. (-1.6849, 1.6849) B. (-17.3330, 13.3330) C. (-1.9047, 1.4652) D. (-16.3950, 14.3950)

h. For a Normal Distribution with mean 0 and standard deviation 4.0, what values leave probability 0.039 in both tails? A. (-5.6746, 5.6746) B. (-7.0496, 7.0496) C. (-2.0642, 2.0642) D. (-8.2567, 8.2567)

i. A regression coefficient is estimated to be equal to -12.684 with standard error 9.4; there are 16 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.1960 B. 0.4810 C. 1.8228 D. 0.9323

j. A regression coefficient is estimated to be equal to 10.030 with standard error 4.0; there are 5 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.2030 B. 0.3354 C. 0.0300 D. 0.0540

k. A regression coefficient is estimated to be equal to 0.559 with standard error 0.2; there are 3 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.6797 B. 0.9320 C. 0.0680 D. 0.7121

l. A regression coefficient is estimated to be equal to -3.564 with standard error 1.9; there are 22 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.2100 B. 0.0740 C. 0.8950 D. 0.9393

7. A Japanese study looked at the effect of "kawaii" (cute) on test performance. (I am inferring numbers from the graphs shown so these might not exactly match the study!) There were 24 subjects; half were shown pictures of cute baby animals and half were shown pictures of full-grown animals (not cute). The ability to complete tasks, for those shown cute pictures, changed by 4, with a standard deviation of 3.5. The ability to complete tasks, for the control group, changed by 0.5 with a standard deviation of 2.9. What is the difference in means? What is the standard error of the difference? What is the normalized value for the difference? What are the degrees of freedom? What is the p-value? Is this difference statistically significant? Comment on the study. Should you immediately Google images of cute baby animals to help the rest of your exam performance?

Nittono H, Fukushima M, Yano A, Moriya H (2012) The Power of Kawaii: Viewing Cute Images Promotes a Careful Behavior and Narrows Attentional Focus. PLoS ONE 7(9): e46362.

8. Consider the BRFSS dataset, the Behavioral Risk Factor Surveillance Study. There are many observations on a wide variety of risky behaviors: smoking, drinking, poor eating, flu shots, whether household has a 3-day supply of food and water... For now concentrate on BMI, which is Body Mass Index, a measure of whether a person is obese. Construct at least one good model to explain BMI. What are descriptive statistics for BMI? Does this suggest some way you ought to limit the sample? What explanatory variables could be in the model? Which are available in the BRFSS data? Construct at least one good regression model; discuss the estimates (including statistical significance but also relevance and whether the estimates accord with theory). How could you improve the model? Consider nonlinear age terms, gender-age interactions, race-age interactions, state dummies and more. Note that INCOME2 is not a continuous variable but you would need to create dummy variables for the relevant income levels.

9. The BRFSS data includes information on household disaster preparedness. Two measures are whether the household has a 3-day supply of food and water. We might believe these to be similar so want to examine the marginal probabilities.

Count
		Water– 3 day supply
		= "Yes"	= "No"
Food – 3 day supply	= "Yes"	5528	3190
	= "No"	484	1130

What is the probability that a household has sufficient food and water for 3 days? Given that a household has sufficient food, what is the probability that it has sufficient water as well? If a household does not have sufficient food, what is the probability that it has sufficient water? Are the latter two proportions statistically significantly different?

10. Continuing with the BRFSS, examine the 0/1 dependent variable of whether the person ever smoked seriously (which they define as at least 100 cigarettes); the variable is SMOKE100. We are interested in de-tangling the effects of both income and education. (Recall note from previous question about INCOM2 variable.) Estimate both probit and logit models; explain different predictions from each model. Explore various specifications possibly including interactions, dummies, etc. Carefully explain the results that you find.

11. You might find it useful to sketch these.

a. For a Normal Distribution with mean 1 and standard deviation 9.6, what is area to the right of 23.1? A. 0.1251 B. 0.0107 C. 0.4585 D. 0.9893

b. For a Normal Distribution with mean 8 and standard deviation 4.9, what is area to the left of 6.5? A. 0.5596 B. 0.7642 C. 0.3821 D. 0.1587

c. For a Normal Distribution with mean 4 and standard deviation 7.1, what is area in both tails farther from the mean than 13.2? A. 0.1936 B. 0.3872 C. 0.2866 D. 0.1587

d. For a Normal Distribution with mean -11 and standard deviation 5.0, what is area in both tails farther from the mean than 0.5? A. 0.1251 B. 0.1587 C. 0.0429 D. 0.0214

e. For a Normal Distribution with mean 13 and standard deviation 3.5, what value leaves probability 0.197 in the left tail? A. 12.0588 B. 10.0166 C. 0.8030 D. 15.9834

f. For a Normal Distribution with mean -10 and standard deviation 2.6, what values leave probability 0.146 in both tails? A. (-1.4538, 1.4538) B. (-5.3000, -2.3923) C. (-13.7799, -6.2201) D. (-8.7799, -1.2201)

g. For a Normal Distribution with mean 12 and standard deviation 9.8, what values leave probability 0.220 in both tails? A. (-1.2265, 1.2265) B. (10.5205, 13.4795) C. (-0.0200, 24.0200) D. (4.4325, 19.5675)

h. A regression coefficient is estimated to be equal to -5.941 with standard error 3.9; there are 9 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.1620 B. 0.8491 C. 0.1080 D. 0.3380

i. A regression coefficient is estimated to be equal to -10.249 with standard error 3.5; there are 26 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.0966 B. 0.9930 C. 0.0070 D. 0.9999

j. A regression coefficient is estimated to be equal to 5.563 with standard error 3.0; there are 24 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.9240 B. 0.0363 C. 0.1710 D. 0.0760

12. Using data from the NHANES study, we find the following numbers of people classified as whether they report themselves to be overweight (person_overweight) and if they have ever tried marijuana (tried_pot).

	person is not overweight	person is overweight
has not tried marijuana	613	837
has tried marijuana	848	956

a) What fraction of people who are overweight have tried marijuana? What fraction of people who are not overweight have tried marijuana?

b) Are these statistically significantly different? What is the p-value of a hypothesis test for a difference in the means?

c) Does this data provide evidence that smoking marijuana helps people not be overweight? Discuss.

13. A study of Quantitative Easing in Japan (Kobayashi, Spiegel, and Yamori 2006) looked at the stock prices of particularly indebted firms to see if they were disproportionately impacted by the Bank of Japan's easy money policy. They report the following (49 Observations and R²=0.08):

	Estimate	T-Statistic	P-Value
Capital	-0.03	-1.879
Liquidity	-0.51	-0.929
Bad Loan	-0.00	-0.066

Where the "Capital" is the capital-asset ratio of the firm's main bank; "Liquidity" is its main bank's ratio of cash, reserves, and loan balances to assets; and "Bad Loan" is the ratio of nonperforming loans to total assets.

a) What are the p-values for each T-statistic?

b) Which regressors are statistically significant?

c) What does this imply?

14. Using the PUMS data for people in NYC, people are classified if they report that they speak English well or very well versus those who do not speak it well or at all. Among the 38,740 households who speak English well, 18.29% have children under 6 years old; for the 14,688 that do not speak English well, 14.46% have children under 6. Also, 38.72% of those who speak English well have children under 17; 35.27% of those who do not speak English well have children under 17.

k. Are these differences statistically significant?

l. What is the p-value for each difference in means?

m. Why do you think we might see this difference?

15. Use the PUMS data for people in NYC (download from Blackboard or InYourClass; pums_NYC_2.zip) examine people's choice of rent or own, as well as how much to pay (the variable "own_rent_frac" gives the fraction of household income that goes to costs of either owning or renting).

n. What fraction of households own their apartment/house/dwelling? What fraction rent? What are some of the important factors that explain this difference?

o. Estimate a limited-dependent variable model to explain the choice to rent or own. What variables should be in this regression? Why might we believe that the "own_rent_frac" variable would be endogenous with the own/rent choice? What variables are statistically significant in this choice? Have you omitted any important variables? What are the predicted probabilities for different representative people? Discuss.

p. Estimate a linear regression to explain the fraction of income going to ownership or rental costs. What variables should be in this regression? What variables are statistically significant? Have you omitted any important variables? Discuss.

1. Answer each question; you might find it useful to make a sketch.

a. A regression coefficient is estimated to be equal to -1.417 with standard error 1.6; there are 30 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.9249 B. 0.7998 C. 0.6240 D. 0.3830

b. A regression coefficient is estimated to be equal to -15.901 with standard error 7.1; there are 3 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.1110 B. 0.9749 C. 0.0001 D. 0.9065

c. A regression coefficient is estimated to be equal to -16.558 with standard error 7.1; there are 8 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.9520 B. 0.1280 C. 0.0002 D. 0.0480

d. A regression coefficient is estimated to be equal to -0.322 with standard error 0.3; there are 29 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 1.0000 B. 0.8378 C. 0.2920 D. 0.7080

e. A regression coefficient has standard error 7.50; there are 9 degrees of freedom. The t-statistic is 1.3730. What is the coefficient? A. 1.8302 B. 10.2972 C. 1.1441 D. 0.8282

f. A regression coefficient has standard error 2.00; there are 9 degrees of freedom. The t-statistic is -1.2381. What is the coefficient? A. -2.4762 B. 0.7321 C. 0.7530 D. -0.5836

g. A regression coefficient has standard error 3.40; there are 22 degrees of freedom. The t-statistic is 2.0265. What is the coefficient? A. 1.9573 B. 0.3132 C. 6.8903 D. 0.6075

h. A regression coefficient is estimated to be equal to -14.943; there are 4 degrees of freedom. The t-statistic is -1.7176. What is the standard error? A. 0.0411 B. 0.8390 C. 8.7000 D. 0.9358

i. A regression coefficient is estimated to be equal to -8.636; there are 4 degrees of freedom. The t-statistic is -2.1590. What is the standard error? A. 0.9473 B. 18.6638 C. 0.0150 D. 4.0000

j. A regression coefficient is estimated to be equal to 7.693; there are 16 degrees of freedom. The t-statistic is 1.5699. What is the standard error? A. 1.8836 B. 4.9000 C. 0.1057 D. 0.4808

2. Suppose a student is answering 50 multiple-choice questions on an exam where each question has 4 choices.

a. If the student guesses randomly, what is the expected number of correct answers? If the questions are worth 2 points each, what is the expected score for a student who is completely ignorant?

b. If a student guesses randomly, what is the standard error of the fraction guessed correctly?

c. What is a 95% confidence interval for scores of students who guess randomly?

d. If a student scores 27 points, what is the probability that the student was guessing randomly?

3. Peter Gordon, in his talk at CCNY, presented results from linear regressions to explain the growth of metropolitan areas. He begins with a simple model to explain population growth from 1990-2000:

	Log Population Growth 1990-2000
	Coefficient	t-stat	p-value
Constant term	-0.0229	-0.12
Population in 1990 (log)	0.0192	1.33
Pop. Density in 1990	-0.0504	-1.65
% in manufacturing	-0.0028	-1.63
R^2	0.57

Where he also includes dummy variables for Census Regions (New England, Mid Atlantic, etc.). There are 79 observations and 67 degrees of freedom.

a. What are the p-values for the 3 coefficients? Are they significant?

The averages and standard deviations are:

	Average	Standard deviation
Population in 1990 (log)	14.52	14.89
Pop. Density in 1990	1.80	1.02
% in manufacturing	18.69	7.75

b. What is the predicted population growth for a metropolitan area that is exactly average?

c. What is the predicted population growth for a metro area that is one standard deviation above average in 1990 population? For a metro area one standard deviation above average in density? In manufacturing concentration?

d. Give a careful explanation for why we would observe coefficients of these signs.

4. Since several groups decided that they wanted to look at changing patterns of interracial marriage, I created a dataset from the CPS 2009, that has information for each spouse (with A_FAMREL=2; note the spouse might be male or female) as well as the race, ethnicity, and citizenship of their partner. This data, cps_2009_spouseinfo_famrel2, is on Blackboard. Estimate a linear regression to explain the person's wage as a function of age. Carefully explain which variables you choose to include in the estimation and why they might be important. Show the regression results and note which coefficient estimates are statistically significant. What results are surprising to you? Which results are not surprising? You might estimate and compare several different models.

5. Please answer the following questions on Blackboard. It might help to make sketches.

a. For a Normal Distribution with mean 9 and standard deviation 9.1, what is area in both tails farther from the mean than -8.3? A. 0.8387 B. 0.0574 C. 0.1587 D. 0.9713

b. For a Normal Distribution with mean 1 and standard deviation 9.6, what is area in both tails farther from the mean than 23.1? A. 0.1251 B. 0.0214 C. 0.4585 D. 0.9893

c. For a Normal Distribution with mean 5 and standard deviation 7.6, what is area in both tails farther from the mean than 14.1? A. 0.2743 B. 0.1587 C. 0.2301 D. 0.4603

d. For a Normal Distribution with mean -14 and standard deviation 2.8, what is area in both tails farther from the mean than -20.4? A. 0.0214 B. 0.8235 C. 0.0429 D. 0.0971

e. For a Normal Distribution with mean -2 and standard deviation 3.8, what values leave probability 0.382 in both tails? A. (-3.6610, -0.3390) B. (-5.3220, 1.3220) C. (0.7331, -4.7331) D. (-3.1409, -0.8591)

f. For a Normal Distribution with mean 13 and standard deviation 3.5, what values leave probability 0.099 in both tails? A. (10.0292, 15.9708) B. (7.2260, 18.7740)C. (0.5785, 12.2990) D. (8.4946, 17.5054)

6. Please answer the following questions on Blackboard.

a. A regression coefficient is estimated to be equal to 10.527 with standard error 8.3; there are 19 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.2200 B. 1.7953 C. 0.1323 D. 0.7800

b. A regression coefficient is estimated to be equal to 0.521 with standard error 0.5; there are 17 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.6380 B. 1.7026 C. 0.3120 D. 0.6988

c. A regression coefficient is estimated to be equal to 2.885 with standard error 1.7; there are 19 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.2423 B. 0.2810 C. 0.9980 D. 0.1060

d. A regression coefficient is estimated to be equal to 1.902 with standard error 1.5; there are 26 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.4410 B. 0.3363 C. 0.9714 D. 0.2160

e. A regression coefficient is estimated to be equal to -7.981 with standard error 4.3; there are 28 degrees of freedom. What is the p-value (from the t-statistic) against the null hypothesis of zero? A. 0.2131 B. 0.1630 C. 0.9547 D. 0.9260

f. A regression coefficient has standard error 5.10; there are 14 degrees of freedom. The t-statistic is -2.3978. What is the coefficient? A. -0.8735 B. 0.9730 C. -0.4571 D. -12.2287

g. A regression coefficient has standard error 9.40; there are 16 degrees of freedom. The t-statistic is -1.3494. What is the coefficient? A. -12.6842 B. -0.0543 C. 0.1772 D. 0.8861

h. A regression coefficient is estimated to be equal to 4.873; there are 12 degrees of freedom. The t-statistic is 0.9093. What is the standard error? A. 5.3588 B. 0.2279 C. 0.4061 D. 0.7702

i. A regression coefficient is estimated to be equal to -4.488; there are 7 degrees of freedom. The t-statistic is -1.8992. What is the standard error? A. 0.8650 B. -0.6411 C. 0.0232 D. 2.3631

7. An economic study modeled the log price of gasoline (each week) as a simple function of the log futures price of the week. In the futures market a firm can buy gasoline at a price set today, to be delivered next month, so we anticipate that this should have some predictive power. The model is , where P_t is this week's price of gasoline (in natural logs) and F_t-1 is the price from the week before (also in natural logs) in the futures market. When I estimate this relationship (slightly different data so no use looking online!) I get the following relationship: , where the standard error of the intercept coefficient is 0.006, the standard error of the slope coefficient is 0.008, and the R²=0.96. (M. Chinn, "Gasoline Prices Implied by Futures," 2012)

a. Is the slope coefficient statistically significant? What is its t-statistic? P-value? What is the null hypothesis and what can you conclude?

b. The most recent price of gas was $4.02. The futures price declined from$2.97 to $2.94 (this is the price at the harbor, some of the difference is transportation cost). What does this recent change imply for the price of gasoline next week? (Careful! Disentangle the logs!)

c. A regression of the log price of diesel fuel on the log of last week's futures price of gasoline gives the result, where the standard error of the intercept coefficient is 0.013, the standard error of the slope coefficient is 0.017, and the R²=0.81. How would you evaluate the predictive power of gasoline futures for diesel prices (note that there are no futures traded for diesel)?

8. An experiment in a bar recorded the amount of alcohol ordered, depending whether the waitress put her hand on the shoulder of the first patron while asking if he wanted a drink. There were 24 pairs of men drinking together; 12 were touched and 12 were not. When the waitress touched one, the average amount drunk by the man touched was 36 oz (standard deviation is 6) and the other man in the group drank 29.6 oz (std. dev. 5). When the waitress did not touch either man, they drank 30.6 (std. dev. 5) and 26.6 oz (std. dev. 5). The units are beer-equivalent ounces. [The standard errors were not explicitly reported in the study, I'm making them up.] (Kaufman & Mahoney, J Social Psychology, 1999)

a. There are two slightly different effects: what is the effect of touching a patron on the shoulder, and what is the effect on the second man who sees his drinking buddy get a touch on the shoulder? What is the standard error of the difference in consumption of the first man in each group (who was actually touched)? What is the t-stat for the null hypothesis test that there was no difference in drinking quantity? P-value? Should the alternative hypothesis be one-sided or two-sided?

b. What is the standard error of the difference in consumption of the second man in each group? What are the t-stat and p-value? Should the alternative hypothesis be one-sided or two-sided? Explain the null hypothesis and your conclusions.

9. A study examined whether people were more likely to lie by email or in person, finding in a study of business students that 24 out of 26 lied when writing an email while 14 out of 22 lied when writing on paper. (The lie was in the context of a fictitious business transaction.) (Naquin, Kurtzberg, Belkin 2010 J Applied Psychology)

a. What is the standard error of the fraction of people lying by email? What is the standard error of the fraction of people lying on paper?

b. What are the t-stat and p-value for the null hypothesis that the medium of communication (email or paper) had no effect on the probability of lying?

10. We use the most recent data to assess the relation between changes in GDP and changes in the unemployment rate (so-called Okun's Law), comparing the relation in the entire period since 1948 with the relation in the period since 1990. Data are from FRED Stats. A regression has the dependent variable as the quarterly change in the unemployment rate (denotedDUR). The independent variable is the quarterly percent growth rate of nominal GDP (denoted %DY). The estimated regression is .

a. Using data for the entire period, 1948-2012, the estimated equation is DUR = 0.37 – 0.22%DY, where the standard error of the intercept is 0.03, the standard error of the slope is 0.02, and the R² is 0.39. Is the slope coefficient statistically significant? What is its t-statistic? P-value?

b. Using data for the period 1990-2012, the estimated equation is DUR = 0.38 – 0.30%DY, where the standard error of the intercept is 0.05, the standard error of the slope is 0.04, and the R² is 0.45. Is the slope coefficient statistically significant? What is its t-statistic? P-value?

c. Compare the two regressions. What are the arguments in favor of using the whole sample versus only more recent data?

d. For the most recent data (first quarter of 2012), GDP growth was 0.93 while UR was -0.4. What was the predicted value from each model for that time? How would you interpret this?

11. Use the data on Blackboard, CPS_finalexam. We want to compare the acquisition of wage income, as a function of education, between native-born and immigrant workers. Examine a regression with wage as the dependent variable, and with age, age-squared, educational attainment dummies (choose which are appropriate), and other reasonable independent variables (as many as you think are appropriate).

a. Estimate two such regressions: one for natives and one for immigrants (explain what subgroup you're examining – all people, workers, fulltime workers?).

b. What are the effects of a college degree for the two groups? (Carefully explain the null hypothesis, t-stat, and p-values before explaining the results of the hypothesis test.)

c. Compare the age-wage profiles for natives and immigrants.

d. If you were to estimate two additional regressions but with the logarithm of wages as dependent variable, how would your conclusions change? Explain the hypothesis tests.

e. How would industry/occupation dummy variables change these results?

f. What other models can you estimate that could be informative – explain.

16. You might sketch a picture.

a. For a Normal Distribution with mean 4 and standard deviation of 1, what is the area to the left of 3.3? 0.484 0.758 0.242 0.363

b. For a Normal Distribution with mean -13 and standard deviation of 7, what is the area to the left of -3.2? 0.162 0.081 0.919 0.758

c. For a Normal Distribution with mean 1 and standard deviation of 4, what is the area to the right of -6.6? 0.829 0.029 0.971 0.057

d. For a Normal Distribution with mean -6 and standard deviation of 2, what is the area to the right of -9.8? 0.057 0.829 0.029 0.971

e. For a Normal Distribution with mean -3 and standard deviation of 5, what is the area to the right of -8? 0.691 0.317 0.841 0.159

f. For a Normal Distribution with mean -12 and standard deviation of 5, what is the area in both tails farther from the mean (in absolute value) than -21.5? 0.057 0.029 0.971 0.351

g. For a Normal Distribution with mean -9 and standard deviation of 5, what is the area in both tails farther from the mean (in absolute value) than -10? 0.579 0.421 0.841 0.087

h. For a Normal Distribution with mean -13 and standard deviation of 8 what value leaves 0.22 in the right tail? -3.188 -3.607 -8.303 -11.792

i. For a Normal Distribution with mean -7 and standard deviation of 5 what value leaves 0.24 in the right tail? -4.026 -6.749 -1.052 -1.125

j. For a Normal Distribution with mean 12 and standard deviation of 2 what value leaves 0.03 in the right tail? 15.110 16.340 13.024 14.048

2. You might sketch a picture.

a. For a t Distribution with sample average of 1.43, standard error of 1.22, and 11 observations, what is the area in both tails, for a null hypothesis of zero mean? 0.133 0.181 0.412 0.266

b. For a t Distribution with sample average of 2.9, standard error of 1.82, and 13 observations, what is the area in both tails, for a null hypothesis of zero mean? 0.068 0.541 0.012 0.135

c. For a t Distribution with sample average of 3.31, standard error of 2.16, and 9 observations, what is the area in both tails, for a null hypothesis of zero mean? 0.009 0.160 0.530 0.080

d. For a t Distribution with sample average of 1.47, standard error of 1.47, and 16 observations, what is the area in both tails, for a null hypothesis of zero mean? 0.332 0.166 0.332 0.161

e. For a t Distribution with 20 observations and standard error of 2.53, what sample mean leaves 0.08 in the two tails, when testing a null hypothesis of zero? 0.922 1.844 3.689 4.666

f. For a t Distribution with 5 observations and standard error of 2.78, what sample mean leaves 0.2 in the two tails, when testing a null hypothesis of zero? 0.738 1.476 4.103 2.952

g. For a t Distribution with 20 observations and standard error of 0.53, what sample mean leaves 0.24 in the two tails, when testing a null hypothesis of zero? 1.211 0.606 0.642 2.422

h. Sample A has mean 4.28, standard error of 0.21, and 4 observations. Sample B has mean 4.99, standard deviation of 0.33, and 23 observations. Test the null hypothesis of no difference. 0.005 0.002 0.906 0.517

i. Sample A has mean 1.6, standard error of 0.68, and 9 observations. Sample B has mean 4.83, standard deviation of 2.81, and 9 observations. Test the null hypothesis of no difference. 0.360 0.009 0.010 0.004

3. You are given the following data on the number of people in the PUMS sample who live in each of the five boroughs of NYC and who commute in each specified manner (where 'other' includes walking, working from home, taking a taxi or ferry or rail).

	Bronx	Manhattan	Staten Is	Brooklyn	Queens
car	5788	2692	5526	10990	16905
bus	3132	2789	1871	4731	4636
subway	6481	13260	279	18951	14025
other	2748	10327	900	6587	4877

a. Find the Joint Probability for drawing, from this sample, a person from Queens who commutes by bus. Find the Joint Probability of a person from the Bronx who commutes by subway.

b. Find the Marginal Probability of drawing, from among the people who commute by subway, someone who lives in Brooklyn. Find the Marginal Probability, of people who commute by bus, someone who lives in the Bronx.

c. Find the Marginal Probability of drawing, from among the people who live in Staten Island, someone who drives a car to work. Find the Marginal Probability, of people in Brooklyn, who commute by subway.

d. Are these two choices (which borough to live in, how to commute) independent? Explain using the definition of statistical independence.

4. To investigate an hypothesis proposed by a student, I got data, for 102 of the world's major countries, on the fraction of the population who are religious as well as the income per capita and the enrollment rate of boys and girls in primary school. The hypothesis to be investigated is whether more religious societies tend to hold back women. I ran two separate models: Model 1 uses girls enrollment rate as the dependent; Model 2 uses the ratio of girls to boys enrollment rates as the dependent. The results are below (standard errors in italics and parentheses below each coefficient):

	Model 1	Model 2	t-stat	p-value
Intercept	137	1.12
	(18)	(0.09)
Religiosity	-0.585	-0.0018
	(0.189)	(0.0009)
GDP per capita	0.00056	0.0000016
	(0.00015)	(0.0000007)

a. Which coefficient estimates are statistically significant? What are the t-statistics and p-values for each?

b. How would you interpret these results?

c. Critique the regression model. How would you improve it?

5. Download the data, "PUMA_nyc_for_exam" from Blackboard, which gives PUMA data on people living in the 5 boroughs. Run a regression that models the variable, "GRPIP," "Gross Rent as Percent of Income," which tells how burdensome are housing costs for different people.

a. What are the mean, median, 25^th, and 75^th percentiles for Rent as a fraction of income? Does this seem reasonable?

b. What is the fraction spent on rent by households in Brooklyn? In Queens? Is the difference statistically significant? Between Brooklyn and the Bronx?

c. What variables might be important in explaining this ratio? Find summary statistics for these variables.

d. Run a regression and interpret the output. Which variables are statistically significant? How do you interpret their coefficients? Are these reasonable?

e. What variables are omitted? How could the regression be improved (using actual real data)? Can you estimate a better model (with squared terms, interaction terms, etc)?

6. A random variable is distributed as a standard normal. (You are encouraged to sketch the PDF in each case.)

a. What is the probability that we could observe a value as far or farther than 1.3?

b. What is the probability that we could observe a value nearer than 1.8?

c. What value would leave 10% of the probability in the right-hand tail?

d. What value would leave 25% in both the tails (together)?

7. Using the CPS 2010 data (on Blackboard, although you don't need to download it for this), restricting attention to only those reporting a non-zero wage and salary, the following regression output is obtained for a regression (including industry, occupation, and state fixed effects) with wage and salary as the dependent variable.

a. Fill in the missing values in the table.

b. The dummy variables for veterans have been split into various time periods to distinguish recent veterans from those who served decades ago. If you knew that the draft ended at about the same time as the Vietnam war, how would that affect your interpretation of the coefficient estimates?

c. Critique the regression: how would you improve the estimates (using the same dataset)?

ANOVA^b
Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	8.201E+13	152	5.395E+11	324.098	.000^a
	Residual	1.639E+14	98479	1.665E+09
	Total	2.460E+14	98631

Coefficients^a
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
1	(Constant)	12970.923	2290.740		5.662	.000
	Demographics, Age	2210.038	62.066	.605	____	____
	Age squared	-21.527	.693	-.504	____	____
	Female	-14892.950	____	-.149	-47.872	.000
	African American	-3488.065	____	-.022	-7.809	.000
	Asian	-2700.032	____	-.012	-2.782	.005
	Native American Indian or Alaskan or Hawaiian	____	824.886	-.009	-3.442	.001
	Hispanic	____	483.313	-.024	-6.847	.000
	Immigrant	____	632.573	-.032	-6.728	.000
	1 or more parents were immigrants	989.451	541.866	.008	____	____
	immig_india	-456.482	1675.840	-.001	____	____
	immig_SEAsia	821.730	1252.853	.003	____	____
	immig_MidE	-599.852	2335.868	-.001	____	____
	immig_China	3425.017	1821.204	.006	____	____
	Education: High School Diploma	2786.569	492.533	.025	5.658	.000
	Education: Some College but no degree	5243.544	528.563	.042	9.920	.000
	Education: Associate in vocational	6530.542	762.525	.028	8.564	.000
	Education: Associate in academic	7205.474	736.838	.032	9.779	.000
	Education: 4-yr degree	17766.941	576.905	.143	30.797	.000
	Education: Advanced Degree	36755.485	703.658	.227	52.235	.000
	Married	4203.602	414.288	.042	10.147	.000
	Divorced or Widowed or Separated	830.032	501.026	.006	1.657	.098
	kids_under18	3562.643	327.103	.036	10.891	.000
	kids_under6	-721.123	404.818	-.006	-1.781	.075
	Union member	4868.240	976.338	.013	4.986	.000
	Veteran since Sept 2001	2081.909	4336.647	.001	.480	.631
	Veteran Aug 1990 - Aug 2001	-1200.688	1788.034	-.002	-.672	.502
	Veteran May 1975-July 1990	-1078.953	1895.197	-.001	-.569	.569
	Veteran August 1964-April 1975	-6377.461	3195.784	-.005	-1.996	.046
	Veteran Feb 1955-July 1964	-7836.420	4904.511	-.004	-1.598	.110
	Veteran July 1950-Jan 1955	-19976.382	10570.869	-.005	-1.890	.059
	Veteran before 1950	-15822.026	12943.766	-.003	-1.222	.222

8. Using the NHANES 2007-09 data (on Blackboard, although you only need to download it for the very last part), reporting a variety of socioeconomic variables as well as behavior choices such as the number of sexual partners reported (number_partners), we want to see if richer people have more sex than poor people. The following table is constructed, showing three categories of family income and 5 categories of number of sex partners:

	number of sex partners
family income	zero	1	2 - 5	6 - 25	>25	Marginal:
< 20,000	11	63	236	255	92	______
20 - 45,000	7	117	323	308	117	______
> 45,000	3	234	517	607	218	______
Marginal:	______	______	______	______	______

a. Where is the median, for number of sex partners, for poorer people? For middle-income people? For richer people?

b. Conditional on a person being poorer, what is the likelihood that they report fewer than 6 partners? Conditional on being middle-income? Richer?

c. Conditional on reporting 2-5 sex partners, what is the likelihood that a person is poorer? Middle-income? Richer?

d. Explain why the average number of sex partners might not be as useful a measure as, for example, the data ranges above or the median or the 95%-trimmed mean.

e. (5 points) (You will need to download the data for this part) Could the difference be explained by schooling effects? How does college affect the number of sex partners?

9. I provide a dataset online (stock_indexes.sav on InYourClass) with the S&P 500 stock index and its daily returns as well as the NASDAQ index and its returns, from January 1, 1980 to December 9, 2010.

a. What is the mean and standard deviation?

b. If the stock index returns were distributed normally, what value of return is low enough, that 95% of the days are better?

c. What is the 5% value of the actual returns (the fifth percentile, use "Analyze\Descriptive Statistics\Explore" and check "Percentiles" in "Options")? Is this different from your previous answer? What does that imply? Explain.

10. Using the CPS 2010 data online, examine whether children are covered by Medicaid or other insurance plan. Run a crosstab on "CH_HI" whether a child has health insurance, and "CH_MC" if a child is covered by Medicaid.

a. What fraction of children are covered by Medicaid? What fraction of children are not covered by any policy?

b. What is the average family income of children who are covered by Medicaid? Of children who are not? What is the t-statistic and p-value for a statistical test of whether the means are equal?

11. The oil and gas price dataset online, (oil_gas_prices.sav on InYourClass, although you only need to download it for the very last part), has data on prices of oil, gasoline, and heating oil (futures prices, in this case). Compare two regression specifications of the current price of gasoline. Specification A explains the current price with its price the day before. Specification B has the price of gas on the day before but also includes the prices of crude oil and heating oil on the day before. The estimates of the coefficient on gasoline are shown below:

	Coefficient estimate	Standard error
Specification A	0.021	0.028
Specification B	0.153	0.048

a. Calculate t-statistics and p-values for each specification of the regression.

b. Explain what you could learn from each of these regressions – specifically, would it be a good idea to invest in gasoline futures?

c. Explain why there is a difference in the estimated coefficients. Can you say that one is more correct?

12. A random variable is distributed as a standard normal. (You are encouraged to sketch the PDF in each case.)

d. What is the probability that we could observe a value as far or farther than -0.9?

e. What is the probability that we could observe a value nearer than 1.4?

f. What value would leave 5% of the probability in the right-hand tail?

g. What value would leave 5% in both the tails (together)?

13. [this question was given in advance for students to prepare with their group} Download (from Blackboard) and prepare the dataset on the 2004 Survey of Consumer Finances from the Federal Reserve. Estimate the probability that each head of household (restrict to only heads of household!) has at least one credit card. Write up a report that explains your results (you might compare different specifications, you might consider different sets of socioeconomic variables, different interactions, different polynomials, different sets of fixed effects, etc.).

14. Explain in greater detail your topic for the final project. Include details about the dataset which you will use and the regressions that you will estimate. Cite at least one previous study which has been done on that topic (published in a refereed journal).

15. You want to examine the impact of higher crude oil prices on American driving habits during the past oil price spike. A regression of US gasoline purchases on the price of crude oil as well as oil futures gives the coefficients below. Critique the regression and explain whether the necessary basic assumptions hold. Interpret each coefficient; explain its meaning and significance.

Coefficients(a)

Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
1	(Constant)	.252	.167		1.507	.134
	return on crude futures, 1 month ahead	.961	.099	.961	9.706	.000
	return on crude futures, 2 months ahead	-.172	.369	-.159	-.466	.642
	return on crude futures, 3 months ahead	.578	.668	.509	.864	.389
	return on crude futures, 4 months ahead	-.397	.403	-.333	-.986	.326
	US gasoline consumption	-.178	.117	-.036	-1.515	.132
	Spot Price Crude Oil Cushing, OK WTI FOB (Dollars per Barrel)	4.23E-005	.000	.042	1.771	.079

a Dependent Variable: return on crude spot price

16. You estimate the following coefficients for a regression explaining log individual incomes:

Coefficients(a)

Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta	B	Std. Error
1	(Constant)	6.197	.026		239.273	.000
	Demographics, Age	.154	.001	1.769	114.120	.000
	agesq	-.002	.000	-1.594	-107.860	.000
	female	-.438	.017	-.184	-25.670	.000
	afam	-.006	.010	-.002	-.590	.555
	asian	-.011	.015	-.002	-.713	.476
	Amindian	-.063	.018	-.009	-3.573	.000
	Hispanic	.053	.010	.016	5.139	.000
	ed_hs	.597	.014	.226	43.251	.000
	ed_smcol	.710	.014	.272	50.150	.000
	ed_coll	1.138	.015	.379	74.378	.000
	ed_adv	1.388	.018	.355	78.917	.000
	Married	.222	.009	.092	25.579	.000
	Divorced Widowed Separated	.138	.011	.041	12.311	.000
	union	.189	.021	.022	8.951	.000
	veteran	.020	.012	.004	1.646	.100
	immigrant	-.055	.013	-.017	-4.116	.000
	2^nd Generation Immigrant	.064	.012	.022	5.268	.000
	female*ed_hs	-.060	.020	-.017	-2.948	.003
	female*ed_smcol	-.005	.020	-.002	-.270	.787
	female*ed_coll	-.104	.022	-.026	-4.806	.000
	female*ed_adv	-.056	.025	-.010	-2.218	.027

a Dependent Variable: lnwage

a. Explain your interpretation of the final four coefficients in the table.

b. How would you test their significance? If this test got "Sig. = 0.13" from SPSS, interpret the result.

c. What variables are missing? Explain how this might affect the analysis.

17. Fill in the blanks in the following table showing SPSS regression output. The model has the dependent variable as time spent working at main job.

Coefficients(a)

Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
1	(Constant)	198.987	7.556		26.336	.000
	female	-65.559	4.031	-.138	___?___	___?___
	African-American	-9.190	6.190	-.013	___?___	___?___
	Hispanic	17.283	6.387	.024	___?___	___?___
	Asian	1.157	12.137	.001	___?___	___?___
	Native American/Alaskan Native	-28.354	14.018	-.017	-2.023	.043
	Education: High School Diploma	___?___	6.296	.140	11.706	.000
	Education: Some College	___?___	6.308	.174	14.651	.000
	Education: 4-year College Degree	110.064	___?___	.183	16.015	.000
	Education: Advanced degree	126.543	___?___	.166	15.714	.000
	Age	-1.907	___?___	-.142	-16.428	.000

a Dependent Variable: Time Working at main job

18. Suppose I were to start a hedge fund, called KevinNeedsMoney Limited Ventures, and I want to present evidence about how my fund did in the past. I have data on my fund's returns, Rett, at each time period t, and the returns on the market, Mktt. The graph below shows the relationship of these two variables:

a. I run a univariate OLS regression, . Approximately what value would be estimated for the intercept term, b₀? For the slope term, b₁?

b. How would you describe this fund's performance, in non-technical language – for instance if you were advising a retail investor without much finance background?

19. Using the American Time Use Study (ATUS) we measure the amount of time that each person reported that they slept. We run a regression to attempt to determine the important factors, particularly to understand whether richer people sleep more (is sleep a normal or inferior good) and how sleep is affected by labor force participation. The SPSS output is below.

Coefficients(a)
Model		Unstandardized Coefficients		Standardized Coefficients
		B	Std. Error	Beta	t	Sig.
1	(Constant)	-4.0717	4.6121		-0.883	0.377
	female	23.6886	1.1551	0.18233	20.508	0.000
	African-American	-8.5701	1.7136	-0.04369	-5.001	0.000
	Hispanic	10.1015	1.7763	0.05132	5.687	0.000
	Asian	-1.9768	3.3509	-0.00510	-0.590	0.555
	Native American/Alaskan Native	-3.5777	3.8695	-0.00792	-0.925	0.355
	Education: High School Diploma	2.5587	1.8529	0.01768	1.381	0.167
	Education: Some College	-0.3234	1.8760	-0.00222	-0.172	0.863
	Education: 4-year College Degree	-1.3564	2.0997	-0.00821	-0.646	0.518
	Education: Advanced degree	-3.3303	2.4595	-0.01590	-1.354	0.176
	Weekly Earnings	0.000003	0.000012	-0.00277	-0.246	0.806
	Number of children under 18	2.0776	0.5317	0.03803	3.907	0.000
	person is in the labor force	-11.6706	1.7120	-0.08401	-6.817	0.000
	has multiple jobs	0.4750	2.2325	0.00185	0.213	0.832
	works part time	4.2267	1.8135	0.02244	2.331	0.020
	in school	-5.4641	2.2993	-0.02509	-2.376	0.017
	Age	1.1549	0.1974	0.31468	5.850	0.000
	Age-squared	-0.0123	0.0020	-0.33073	-6.181	0.000

a. Which variables are statistically significant at the 5% level? At the 1% level?

b. How much more or less time (in minutes) would be spent sleeping by a male college graduate who is African-American and working full-time, bringing weekly earnings of $1000?

c. Are there other variables that you think are important and should be included in the regression? What are they, and why?

20. You are given the following output from a logit regression using ATUS data. The dependent variable is whether the person spent any time cleaning in the kitchen and the independent variables are the usual list of race/ethnicity (African-American, Asian, Native American, Hispanic), female, educational attainment (high school diploma, some college, a 4-year degree, or an advanced degree), weekly earnings, the number of kids in the household, dummies if the person is in the labor force, has multiple jobs, works part-time, or is in school now, as well as age and age-squared. We include a dummy if there is a spouse or partner present and then an interaction term for if the person is male AND there is a spouse in the household. There are only adults in the sample. Descriptive statistics show that approximately 5% of men clean in the kitchen while 20% of women do. The SPSS output for the logit regression is:

	B	S.E.	Wald	df	Sig.	Exp(B)
female	0.9458	0.0860	120.945	1	0.000	2.5749
African-American	-0.6113	0.0789	60.079	1	0.000	0.5427
Hispanic	-0.2286	0.0765	8.926	1	0.003	0.7956
Asian	0.0053	0.1360	0.001	1	0.969	1.0053
Native American	-0.0940	0.1618	0.338	1	0.561	0.9103
Education: high school	0.0082	0.0789	0.011	1	0.917	1.0082
Education: some college	0.0057	0.0813	0.005	1	0.944	1.0057
Education: college degree	0.0893	0.0887	1.013	1	0.314	1.0934
Education: advanced degree	0.0874	0.1009	0.751	1	0.386	1.0914
Weekly Earnings	0.0000007	0.0000005	1.943	1	0.163	1.0000
Num. Kids in Household	0.2586	0.0226	131.473	1	0.000	1.2952
person in the labor force	-0.5194	0.0694	55.967	1	0.000	0.5949
works multiple jobs	-0.2307	0.1009	5.223	1	0.022	0.7940
works part-time	0.1814	0.0733	6.130	1	0.013	1.1989
person is in school	-0.1842	0.1130	2.658	1	0.103	0.8318
Age	0.0551	0.0088	38.893	1	0.000	1.0567
Age-squared	-0.0004	0.0001	22.107	1	0.000	0.9996
spouse is present	0.5027	0.0569	78.074	1	0.000	1.6531
Male * spouse is present	-0.6562	0.1087	36.462	1	0.000	0.5188
Constant	-3.3772	0.2317	212.434	1	0.000	0.0341

a. Which variables from the logit are statistically significant at the 5% level? At the 1% level?

b. How would you interpret the coefficient on the Male * spouse-present interaction term? What is the age when a person hits the peak probability of cleaning?

21. Use the SPSS dataset, atus_tv from Blackboard, which is a subset of the American Time Use survey. This time we want to find out which factors are important in explaining whether people spend time watching TV. There are a wide number of possible factors that influence this choice.

a. What fraction of the sample spend any time watching TV? Can you find sub-groups that are significantly different?

b. Estimate a regression model that incorporates the important factors that influence TV viewing. Incorporate at least one non-linear or interaction term. Show the SPSS output. Explain which variables are significant (if any). Give a short explanation of the important results.

22. This question refers to your final project.

d. What data set will you use?

e. What regression (or regressions) will you run? Explain carefully whether the dependent variable is continuous or a dummy, and what this means for the regression specification. What independent variables will you include? Will you use nonlinear specifications of any of these? Would you expect heteroskedasticity?

f. What other variables are important, but are not measured and available in your data set? How do these affect your analysis?

23. Estimate the following regression:: S&P100 returns = b0 + b1(lag S&P100 returns) + b2(lag interest rates) + ε

using the dataset, financials.sav. Explain which coefficients (if any) are significant and interpret them.

24. A study by Mehran and Tracy examined the relationship between stock option grants and measures of the company's performance. They estimated the following specification:

Options = b0+b1(Return on Assets)+b2(Employment)+b3(Assets)+b4(Loss)+u

where the variable (Loss) is a dummy variable for whether the firm had negative profits. They estimated the following coefficients:

	Coefficient	Standard Error
Return on Assets	-34.4	4.7
Employment	3.3	15.5
Assets	343.1	221.8
Loss Dummy	24.2	5.0

Which estimate has the highest t-statistic (in absolute value)? Which has the lowest p-value? Show your calculations. How would you explain the estimate on the "Loss" dummy variable?

25. A paper by Farber examined the choices of how many hours a taxidriver would work, depending on a number of variables. His output is:

"Driver Effects" are fixed effects for the 21 different drivers.

a. What is the estimated elasticity of hours with respect to the wage?

b. Is there a significant change in hours on rainy days? On snowy days?

26. A paper by Gruber looks at the effects of divorce on children (once they become adults), including whether there was an increase or decrease in education and wages. Gruber uses data on state divorce laws: over time some states changed their laws to make divorce easier (no-fault or unilateral divorce). Why do you think that he used state-level laws rather than the individual information (which was in the dataset) about whether a person's parents were divorced? Is it important that he documents that states with easier divorce laws had more divorces? If he ran a regression that explained an adult's wage on the usual variables, plus a measure of whether that person's parents had been divorced, what complications might arise? Explain.

27. Using the data on New Yorkers in 1910, we estimate a binary logistic (logit) model to explain labor force participation (whether each person was working for pay) as a function of gender (a dummy variable for female), race (a dummy for African-American), nativity (a dummy if the person is an immigrant and then another dummy if they are second-generation – their parents were immigrants), marital status (three dummies: one for married; one for Divorced/Separated; one for Widow(er)s), age, age-squared, and interaction effects. We allow interactions between Female and Married (fem_marr = Married * Female), and then between Age and Immigrant (age_immig = Age * Immigrant) and Age-Squared and Immigrant (agesq_immig = Age2 * Immigrant). Explain the following regression results:

Variables in the Equation

		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	female	-1.890	.122	240.805	1	.000	.151
	AfricanAmer	2.703	.235	132.625	1	.000	14.919
	Married	1.144	.193	35.245	1	.000	3.141
	fem_marr	-4.946	.209	562.000	1	.000	.007
	DivSep	.251	.568	.195	1	.658	1.285
	Widow	-1.238	.131	89.790	1	.000	.290
	immigrant	1.575	1.167	1.822	1	.177	4.831
	immig2g	.068	.117	.338	1	.561	1.070
	Age	.114	.047	5.858	1	.016	1.121
	age_sqr	-.00176	.001	7.137	1	.008	.998
	age_immig	-.035	.068	.263	1	.608	.966
	agesq_immig	0.00027	.001	.080	1	.777	1.000
	Constant	1.069	.795	1.809	1	.179	2.911

a Variable(s) entered on step 1: female, AfricanAmer, Married, fem_marr, DivSep, Widow, immigrant, immig2g, age, age_sqr, age_immig, agesq_immig.

At what age do natives peak in their labor force participation? Immigrants? Which is higher? The regression shows that women are less likely to be in the labor force, married people are more likely, African-Americans are more likely, and immigrants are more likely to be in the labor force. Interpret the coefficient on the female-married interaction.

28. Calculate the probability in the following areas under the Normal pdf with mean and standard deviation as given. You might usefully draw pictures as well as making the calculations. For the calculations you can use either a computer or a table.

a. What is the probability, if the true distribution has mean -15 and standard deviation of 9.7, of seeing a deviation as large (in absolute value) as -1?

b. What is the probability, if the true distribution has mean 0.35 and standard deviation of 0.16, of seeing a deviation as large (in absolute value) as 0.51?

c. What is the probability, if the true distribution has mean -0.1 and standard deviation of 0.04, of seeing a deviation as large (in absolute value) as -0.16?

29. Using data from the NHIS, we find the fraction of children who are female, who are Hispanic, and who are African-American, for two separate groups: those with and those without health insurance. Compute tests of whether the differences in the means are significant; explain what the tests tell us. (Note that the numbers in parentheses are the standard deviations.)

	with health insurance	without health insurance
female	0.4905 (0.49994) N=7865	0.4811 (0.49990) N=950
Hispanic	0.2587 (0.43797) N=7865	0.5411 (0.49857) N=950
African American	0.1785 (0.38297) N=7865	0.1516 (0.35880) N=950

30. Explain the topic of your final project. Carefully explain one regression that you are going to estimate (or have already estimated). Tell the dependent variable and list the independent variables. What hypothesis tests are you particularly interested in? What problems might arise in the estimation? Is there likely to be heteroskedasticity? Is it clear that the X-variables cause the Y-variable and not vice versa? Explain. [Note: these answers should be given in the form of well-written paragraphs not a series of bullet items answering my questions!]

31. In estimating how much choice of college major affects income, Hamermesh & Donald (2008) send out surveys to college alumni. They first estimate the probability that a person will answer the survey with a probit model. They use data on major (school of education is the omitted category), how long ago the person graduated, and some information from their college record. Their results are (assume that the 0 coefficient is 0.253):

		pr(respond to survey)	t-statistic
Major (Dummy variable)	Architecture and Fine Arts	-0.044	1.61
	Business---general	0.046	1.72
	Business---quantitative	0.038	1.45
	Communications	0.023	1.00
	Engineering	0.086	2.51
	Humanities	-0.013	0.54
	"Honors"	0.087	2.08
	Social Sciences	0.052	2.28
	Natural Sciences, Pharmacology	0.04	1.52
	Nursing, Social Work	0.061	1.57
dummy variables	Class of 1980	0.025	1.61
	Class of 1985	-0.009	0.61
	Class of 1990	0.041	2.65
	Class of 1995	0.033	2.20
	GPA	0.027	2.59
	Upper Div. Sci. & Math Credits	0.0001	0.21
	Upper Div. Sci. & Math Grades	0.002	0.51
	HS Area Income ($000)	0.001	1.92
	Female	0.031	3.06

What is the probability of reply for a major in quantitative Business, from the Class of 1995, with a GPA of 3.1, with 31 upper-division Science & Math credits, with a 2.9 GPA within those upper-division Science & Math courses, from a high school with a 40 HS Area Income? How much more or less is the probability, if the respondent is female?

32. Consider the following regression output, from a regression of log-earnings on a variety of socioeconomic factors. Fill in the blanks in the "Coefficients" table. Then calculate the predicted change in the dependent variable when Age increases from 25 to 26; then when Age changes from 55 to 56 (note that Age_exp2 is Age2 and Age_exp3 is Age3).

Model Summary

Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.613	.376	.376	.94098

ANOVA

Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	53551.873	26	2059.687	2326.152	.000(a)
	Residual	88995.531	100509	.885
	Total	142547.403	100535

Coefficients(a)

Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
	(Constant)	3.841	0.059		65.581	0.000
	Education: High School Diploma	0.106	0.008	0.040305	__?__	__?__	ß
	Education: AS vocational	__?__	0.015	0.051999	19.644	0.000	ß
	Education: AS academic	0.344	__?__	0.062527	23.574	0.000	ß
	Education: 4 year College Degree	0.587	0.009	0.195326	65.257	0.000
	Education: Advanced Degree	0.865	0.011	0.221309	77.658	0.000
	geog2	0.070	0.013	0.017072	5.220	0.000
	geog3	0.005	0.013	0.001232	__?__	__?__	ß
	geog4	-0.050	0.013	-0.01345	__?__	__?__	ß
	geog5	0.062	0.012	0.019974	__?__	__?__	ß
	geog6	-0.061	0.017	-0.01039	__?__	__?__	ß
	geog7	0.026	0.014	0.006106	__?__	__?__	ß
	geog8	0.056	0.013	0.014445	4.303	0.000
	geog9	0.102	0.012	0.030892	8.357	0.000
	Married	__?__	0.009	0.062911	17.213	0.000	ß
	Widowed	__?__	0.025	-0.00191	-0.697	__?__	ß
	Divorced or Separated	__?__	0.012	0.022796	7.042	0.000	ß
	female	__?__	0.006	-0.19408	-76.899	0.000	ß
	union	0.208	__?__	0.024531	9.808	0.000	ß
	hispanic	-0.106	__?__	-0.03211	-12.012	0.000	ß
	Af_Amer	-0.038	__?__	-0.00995	-3.774	0.000	ß
	NativAm	-0.100	__?__	-0.01342	-5.322	0.000	ß
	AsianAm	-0.061	__?__	-0.01147	-4.420	0.000	ß
	MultRace	0.001	0.066	1.93E-05	0.008	__?__	ß
	Demographics, Age	0.377	0.005	4.332516	83.265	0.000
	Age_exp2	-0.00689	0.00011	-6.70717	-65.345	0.000
	Age_exp3	0.0000384	0.0000008	2.65889	49.301	0.000

a Dependent Variable: ln_earn

33. Use the dataset brfss_exam2.sav. This has data from the Behavioral Risk Factors Survey, focused on people under 30 years old. Carefully estimate a model to explain the likelihood that a person has smoked (measured by variable "eversmok"). Note that I have created some basic dummy variables but you are encouraged to create more of your own, as appropriate. Explain the results of your model in detail. Are there surprising coefficient estimates? What variables have you left out (perhaps that aren't in this dataset but could have been collected), that might be important? How is this omission likely to affect the estimated model? What is the change in probability of smoking, between a male and female (explain any other assumptions that you make, to calculate this)?

34. Using the CPS 2010 data (you don't need to download it for this), restricting attention to only prime-age (25-55 year-old) males reporting a non-zero wage and salary, the following regression output is obtained for a regression (including industry, occupation, and state fixed effects) with log wage and salary as the dependent variable.

a. (17 points) Fill in the missing values in the table.

b. (3 points) Critique the regression: how would you improve the estimates (using the same dataset)?

Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	11194.359	145	77.202	127.556	.000^a
	Residual	21558.122	35619	.605
	Total	32752.482	35764

Coefficients^a
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
1	(Constant)	8.375	.112		74.714	.000
	Demographics, Age	.078	.005	.705
	Age squared	-.00085	.00006	-.617
	African American	-.184	.015	-.058
	Asian		.022	-.025	-4.620	.000
	Native American Indian or Alaskan or Hawaiian		.027	-.025	-5.674	.000
	Hispanic	-.051		-.020	-2.172	.030
	Mexican	-.021		-.007	-.868	.386
	Puerto Rican	.014		.002	.319	.750
	Cuban	.007	.059	.001
	Immigrant	-.094	.019	-.039
	1 or more parents were immigrants	.001	.018	.001
	Education: High School Diploma	.219		.105	13.582	.000
	Education: Some College but no degree	.333		.130	18.332	.000
	Education: Associate in vocational	.362		.081	14.919	.000
	Education: Associate in academic		.025	.080	14.642	.000
	Education: 4-yr degree		.019	.236	28.773	.000
	Education: Advanced Degree		.023	.253	33.757	.000
	Married		.011	.140	25.219	.000
	Divorced or Widowed or Separated		.016	.021	3.992	.000
	Union member		.030	.031	7.168	.000
	Veteran since Sept 2001	-.047	.094	-.002
	Veteran Aug 1990 - Aug 2001	-.053	.038	-.006
	Veteran May 1975-July 1990	.035	.048	.003
	Veteran August 1964-April 1975	.078	.129	.003

35. Using the BRFSS 2009 data, the following table compares the reported health status of the respondent with whether or not they smoked (defined as having at least 100 cigarettes)

		SMOKED AT LEAST 100 CIGARETTES
		Yes	No	Marginal
GENERAL HEALTH	Excellent	27775	49199	____
	Very good	58629	77357	____
	Good	64237	67489	____
	Fair	31979	26069	____
	Poor	15680	9191	____
	Marginal	____	____

a. What is the median health status for those who smoked? For non-smokers?

b. Fill in the marginal probabilities – make sure they are probabilities.

c. Explain what you might conclude from this data.

36. Using the CPS data, run at least 4 interesting regressions to model the wages earned. Carefully explain what we can learn from each regression: does it accord with theory; if not, what does this mean? Explain what statistical measures allow us to compare different specifications.

37. For a Normal Distribution with mean 9 and standard deviation 9.1, what is area to the right of -8.3?

A. 0.8387 B. 0.9713 C. 0.1587 D. 0.0287

38. For a Normal Distribution with mean 1 and standard deviation 9.6, what is area to the right of 23.1?

A. 0.1251 B. 0.0107 C. 0.4585 D. 0.9893

39. For a Normal Distribution with mean 12 and standard deviation 7.9, what is area to the right of 30.2?

A. 0.1587 B. 0.9893 C. 0.9356 D. 0.0107

40. For a Normal Distribution with mean 5 and standard deviation 7.6, what is area to the right of 14.1?

A. 0.2743 B. 0.1587 C. 0.1151 D. 0.2301

41. For a Normal Distribution with mean -14 and standard deviation 2.8, what is area to the left of -20.4?

A. 0.0107 B. 0.8235 C. 0.0214 D. 0.0971

42. For a Normal Distribution with mean -2 and standard deviation 3.8, what is area to the left of 2.9?

A. 0.7007 B. 0.9032 C. 0.1936 D. 0.2578

43. For a Normal Distribution with mean 4 and standard deviation 7.1, what is area to the left of 13.2?

A. 0.9032 B. 0.1936 C. 0.2866 D. 0.1587

44. For a Normal Distribution with mean -11 and standard deviation 5.0, what is area to the left of 0.5?

A. 0.1251 B. 0.1587 C. 0.0214 D. 0.9893

45. For a Normal Distribution with mean -7 and standard deviation 5.1, what is area in both tails farther from the mean than -1.9?

A. 0.3173 B. 0.0849 C. 0.6346 D. 0.9151

46. For a Normal Distribution with mean 13 and standard deviation 3.5, what is area in both tails farther from the mean than 7.8?

A. 0.2672 B. 0.1336 C. 0.1587 D. 0.7734

47. For a Normal Distribution with mean 10 and standard deviation 5.9, what is area in both tails farther from the mean than 11.2?

A. 0.8415 B. 0.4602 C. 0.1587 D. 0.5793

48. For a Normal Distribution with mean 1 and standard deviation 7.8, what is area in both tails farther from the mean than 18.2?

A. 0.0278 B. 0.9861 C. 0.1587 D. 0.1357

49. For a Normal Distribution with mean -5 and standard deviation 1.6, what value leaves probability 0.794 in the left tail?

A. NaN B. 0.2060 C. -3.6874 D. 0.8204

50. For a Normal Distribution with mean -7 and standard deviation 6.5, what value leaves probability 0.689 in the left tail?

A. -3.7954 B. -5.3977 C. -10.2046 D. 0.4930

51. For a Normal Distribution with mean 12 and standard deviation 1.5, what value leaves probability 0.825 in the left tail?

A. 0.1750 B. 13.4019 C. 8.9346 D. 0.9346

52. For a Normal Distribution with mean -12 and standard deviation 9.6, what value leaves probability 0.006 in the left tail?

A. -2.5121 B. 12.1166 C. -33.6684 D. -36.1166

53. For a Normal Distribution with mean -2 and standard deviation 9.1, what value leaves probability 0.182 in the right tail?

A. 0.9078 B. 6.2607 C. -1.1275 D. 0.8180

54. For a Normal Distribution with mean 0 and standard deviation 4.0, what value leaves probability 0.077 in the right tail?

A. -4.0777 B. -5.7022 C. 1.4255 D. 5.7022

55. For a Normal Distribution with mean 13 and standard deviation 4.9, what value leaves probability 0.489 in the right tail?

A. 13.1351 B. 0.0276 C. 12.9324 D. 12.8649

56. For a Normal Distribution with mean -3 and standard deviation 1.0, what value leaves probability 0.133 in the right tail?

A. 1.1123 B. -3.6250 C. -4.1123 D. -1.8877