Instructions. This is an open book, open note exam.  Time limit: 3 hours.  The variables for the problems are listed below.    Other constructed variables are included with the individual outputs. Please show the formulas you are using and put any discussions into the context of the specific problem. Please try to  carry  three  significant  figures  when  working  calculations.     A  calculator  should   be  used  for computations as needed. Please watch your time. There are 20 sub-questions (5 points each) so you will have 9 minutes on average for each sub-question. Some questions will take much less than 9 minutes, some more. Please try to answer each question as I can provide no partial credit with nothing written.

Questions 1 -8 use a Wooldridge data set “Sleep75” . Appendix 1 lists 40 observations of the 706         observations in the data set and an analysis of the data including two variables generated just before the data is listed.   The variables are:

sleep                    Number of minutes per sleep per week at night

totwrk                  Minutes worked per week

age                        Age in years

educ                      Number of years of schooling in years

marr                      =1 if married; otherwise =0

gdhlth                   =1 if excellent or good health

clerical                  =1 if clerical worker

construc              =1 if a construction worker

1.           Regression #1 on Page 3 sets out to explain the minutes per week of nightly sleep in terms of a  number of variables.  Write out the model estimated (you do not need all the assumptions).       Using that model, write out the hypothesis being testing with the F statistics computed.  Draw a picture of the distribution and test that hypothesis with α=.01.

2.           Regression #2 on Page 4 adds two constructed variables.  What is the name of this test; what is being tested; and what are your conclusions?  Use α=.10 and show a picture of the distribution to describe your conclusion.

3.           Suppose a student enrolls in the MIEF program at age 25.  After one year in the program, what is the change in sleep predicted using Regression #3 on page 5  Put that number into words.            Assuming 16 years of education prior to enrolling in the MIEF program, what is the change in       sleep predicted after one year in the program using Regression #3 on Page 5?  Put that number   into words.

Continuing with Regression #3 on Page 5, put into words the constant and the coefficient on clerical.

Using Regression #4 on Page 5, put in words the change in sleep based on one additional year of education.

Using Regression #4 on Page 5, Regression #6 on Page 7, and Regression #7 on Page 8,                 determine (using the SSR version of the formula)  if the function in Regression #4 is different for men and women.  Use α=.10 in your analysis with a clear picture of the probability distribution  and your conclusion shown on the picture.

Using Regression #4 on Page 5 and Regression #5 on Pages 6 and 7, determine (using the R          squared version of the formula) if the function in Regression #4 is different for men and women. .  Use α=.10 in your analysis with a clear picture of the probability distribution and your                conclusion shown on the picture.

Following Regression #8 on page 8 is the calculation of residuals and the listing of those            residuals on Page 9.  Describe those residuals clearly.  State the slope coefficient in Regression #9 on Page 10 and put that number into words from Regression #9 and from Regression #4 on

Page 5.

Questions 9 through 17 use a Wooldridge data set “airplane” that consists of data on a large number of airline routes for the years 1997, 1998, 1999, and 2000.  Only the data for 1997 and 2000 are used in     this analysis.   See page 1 of Appendix 2 for the first 40 observations.   The variables are:

fare                                    average one-way fare ($)

year                                   1997 or 2000

Id                                            route identifier (1 to 1147 – therefore 2298 observations)

dist                                        distance in miles

passen                                  average number of passengers per day

bmktshr                               fraction of market, biggest carrier (ie, big market share)

y00                                        =1 if year == 2000, otherwise = 0

lfare                                       log (fare) – Not shown

ldist                                       log(dist) – Not shown

y00bmkshr                        y00 * bmkshr

9.           Regression #1 on Page 2 of Appendix 2  produces a 95 percent confidence interval for the          population coefficient on passen.   Compute a 99 percent confidence interval.  Explain why it is narrower or wider.  Please show a clear picture of the probability distribution.

10.        State in symbols and words the homoscedasticity assumption when Regression 1 was carried     out.   Regression #2 and  Regression #3 on page 3 are run testing whether the homoscedasticity

assumption was violated.   State clearly the names of these two tests and the assumptions         involved for each test.  What is your conclusion from these two tests?  From Regression #2, can you tell which variable is causing the problem?  Explain briefly.

11.         Regression #4 on page 4 uses the same variables as Regression #1.  Write down the function      estimated from Regression #1 and Regression #4 with the standard errors from each regression written appropriately below each slope coefficient.   Describe briefly why the standard errors    from Regression #4 are more appropriate than the standard errors reported in Regression #1.

12.         Discuss the assumptions made with Regression #5 on page 4.   Do you think those assumptions are appropriate?  Discuss briefly the variables that are used in this regression.

13.         Using Regression #6 and Regression #7 on page 5 along with Regression #1 on page 2, carry out a Chow Test (the SSR version) to see if the coefficients on the function estimating fare changed in 2000 as compared with 1997.

14.         Regression #8 on page 6 adds two additional variables.  Explain clearly the meaning of the constant, the coefficient on bmktshr, and the coefficients on the two new variables.

15.         Regression #9 on page 6 is used to for a prediction of fare.  Calculations following that function   continue on page 7 and page 8.  What values of the independent variables are being used for      this prediction?  What is the point prediction?  What is the standard error of the mean                  prediction?  What does that tell us?  What is the standard error of the individual prediction?        What does that tell us?  A confidence interval for prediction was computed.  Put that confidence interval into words.

16.         Regression #10 on page 8 uses variables described on page 2 of the test questions.   Put in        words  the slope coefficients on ldist and bmktshr.   Where appropriate calculate two values of the impact of the independent variable on the dependent variable.

17.         Page 9 carries out some rearrangement of the data to prepare to carry out Regression #11 on   page 10.  Discuss briefly what type of data is being constructed and how that data is used in      Regression #11.  What are the assumptions made in Regression #11.   What happened to the    variable “dist”?  What other variable might have been appropriate to include in the analysis      from Regression #1 through Regression #10 and how would that variable be dealt with in           Regression #11?  What assumption of OLS would be violated if there were another appropriate variable that was correlated with one of the independent variables in Regression #1?

Questions 18– 20 use the analysis in Appendix 3 involving quarterly data from 2002 to 2019 taken from the Federal Reserve Bank of St. Louis (FRED Data).  The data is listed on pages 1-2. The variables are:

DATE                                     Quarterly identifier

Sequence                            Sequence numbers

Real_GPDI                           Real Gross Private Domestic Investment (2012 $) Not Seasonally

Adjusted (Billions of US$)

Real_GDP                            Real Gross Domestic Production  (2012 $) Not seasonally Adjusted

(Billions of US$)

Bond                                     Long-Term Government Bond Yields (10-year) Not Seasonally Adjusted

Real_ Exports                      Real Exports of Goods and Services (2012 $) Not Seasonally Adjusted

(Billions of US$)

Q1                                          =1 if observation is first quarter, =0 otherwise

Q2                                          =1 if observation is second quarter, =0 otherwise

Q3                                          =1 if observation is third quarter, =0 otherwise

Q4                                        =1 if observation is fourth quarter, =0 otherwise

18.         Put in words the coefficient on Real_Exports and Q2 for Regression #1 on Page 3.

19          Put in words the regression coefficient for Regression #2 on page 3 and for Regression #3 on page 4.  You should have two values for the coefficient for Regression #3. (Show any              calculations)

20.         From Regression #4 on Page 4, put in words the coefficient on Real_GDP and l2.Real_Exports. Graph the lag distribution.

Appendix 1

. gen ageeduc = age*educ

. gen educsq = educ^2

. list sleep totwrk age educ ageeduc educsq marr gdhlth  in 21/56,clean

. list clerical construc  male   in 21/60,clean

clerical   construc   male

21.           0           0      1

22.           0           0      1

23.           0           0      1

24.           0           0      1

25.           0           0      1

26.           0           0      1

27.           0           0      1

28.           1           0      0

29.           0           0      1

30.           0           0      1

31.           0           0      1

32.           0           1      1

33.           0           0      1

34.           0           0      1

35.           0           0      1

36.           0           0      1

37.           0           0      1

38.           0           0       1

39.           0           0      1

40.           1           0      1

41.           0           0      1

42.           0           0      1

43.           0           0      0

44.           0           0      1

45.           0           0      1

46.           0           1      1

47.           0           0      1

48.           0           0      1

49.           0           0      1

50.           0           0      1

51.           0           0      1

52.           0           0      1

53.           0           0      1

54.           0           0      1

55.           0           0      1

56.           0           0      0

57.           0           0      1

58.           0           0      1

59.           0           0      1

60.           0           0      1

. /*  Regression #1   */

. reg sleep totwrk age educ  marr male

Source	SS df MS
Model Residual	17023253.9 122216582	5  3404650.77 700  174595.117
Total	139239836       705  197503.313

Number of obs

F(5, 700)

Prob > F

R-squared

Adj R-squared

=

=

=

=

=

=

706

19.50

0.0000

0.1223

0.1160

417.85

sleep			Coef .	Std . Err .	t	P> |t |	[95% Conf .	Interval]
totwrk	- .	1	645387	.0180512	-9 .12	0.000	- .1999797	- .1290978
age	1	.	968593	1.443443	1.36	0.173	- .8654036	4.80259
educ	-1	1	.59746	5.872449	-1 .97	0.049	-23 .12718	- .0677333
marr	3	0	.35958	41.88	0.72	0.469	-51 .86588	112.585
male	8	3	.13675	34.98239	2.38	0.018	14.45376	151.8197
_cons	3	6	15.422	117.9382	30.66	0.000	3383.867	3846.977

. predict sleephat,xb

. generate sleephatsquared = sleephat^2

. generate sleephatcubed = sleephat^3

. /*  Regression #2   */

. reg sleep totwrk age educ  marr gdhlth  male sleephatsquared sleephatcubed