Instructions. This is an open book, open note exam.  Please handwrite your answers on plain paper or  lined notebook paper.  Please refer to any books or notes on a computer or notebook that you wish.      Please do watch your time.  For any calculations you are asked to carry out, please use 3 to 4 significant figures (not more, not less).   Please write formulas and show calculations where necessary; draw           pictures of probability distributions as appropriate.

Please copy the following statement at the beginning of the first page of your answers which is in addition to the Honor Code quiz:

I will complete this assessment in accordance with the rules and spirit of the school’s Honor Code and Academic Integrity Policy as outlined in the Red Book.  I will not receive or give assistance to another  student completing this assessment, not will I consult any internet resources, or other unauthorized   materials before, during, or after the test.

The questions below lead you through an analysis of the Stata computer output contained in two exam appendices.  Each question is worth 5 points so please try to answer all questions.   Please watch your  time.  You have 4.5 hours for the exam.  Assuming you use 30 minutes to scan and upload your written answers, you will have 4 hours or 240 minutes or 12 minutes per question on average.  Keep in mind     that some questions will take longer than other questions to answer.

Questions 1 through 16 use the data and analysis from Appendix 1 which is based on a modified               Wooldridge data set “airplane” that consists of data on a large number of airline routes. The data for     2017 and 2020 are used in this analysis.   See page 1 for the first 40 observations for 2020 and page 13   for both years listed.   Questions 1-14 use only the data for 2020.  Questions 15-18 use the data for both time periods. The variables are:

fare                                    average one-way fare ($)

year                                   2017 or 2020

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)

y20                                      =1 if year == 2020, otherwise = 0

Note:  Other variables are computed in the Stata output

Questions 1-18 use Appendix 1

1.            Regression #1 on Page 2 sets out to explain fare in terms of the distance (dist), number of         passengers on that route per day (passen), and a measure of competition on a route (bmktshr). Write out the function estimated with standard errors and t-values in parentheses.   Put in         words the regression coefficient on dist and  bmktshr (pay attention to the units of bmktshr).    Put in words the R squared

2.           Regression #1 continued.   Stata 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.

3.           Regression #1 continued.  What hypothesis is being tested with the F statistic displayed?  Show the hypothesis test with a picture and critical F value (use α = .01).

4.           Following Regression #1 are some predictions and other calculations and a listing of some of the values below and on page 3, including the r variable.  Describe the r variable and what this tells  you about certain airline routes.

5.           Regression #2 on page 3 carries out a test.  What is this test called, what is it testing, and what conclusions do you draw from this test?

6.           Some new variables were computed on the top of page 4 and added to those in Regression #1 leading to Regression #3 on page 4.  Write out the function estimated with the standard errors below each slope coefficient. (Leave space for an additional standard errors).   Discuss the         statistical significance of the two new variables and what that says about the functional form.  Compare the adjusted R squared between Regression #1 and Regression #3.  What role did the statistical significance plan in that change? Using Regression #3, if there is a route with 500       passengers per day, and the number of  passengers increases by one, what is the predicted       increase in the fare?

7.           Consider a route with dist = 1000 and bmktshr =.5.  Using Regression #3 on page 4, compute the predicted change in fare when dist increases by 1.  Continuing using Regression #3 on page 4,     compute the predicted change in fare when bmktshr increases by 1.

8.           State in symbols and words the homoscedasticity assumption when Regression #3 was carried  out.   Regression 4 and 5 on pages 4 and 5 are run testing whether the homoscedasticity            assumption was violated.   State clearly the names of these two tests and the assumptions        involved for each test.  From Regression #4, can you tell which variable is causing the problem? Explain briefly.

9.           Regression #6 on page 5 uses the same variables as Regression #3.  Go back to Question 6 and    add the standard errors from Regression #6 written appropriately below each standard error for each slope coefficient.   Describe briefly why the standard errors from Regression #6 are more    appropriate than the standard errors reported in Regression #1.

10.         Discuss the assumptions made with Regression #7 on page 6.   Do you think those assumptions  are appropriate?  Regression #8 on page 6 and Regression #9 on page 7 follow.  Explain why       Regression #9 is better than Regression #7 (if it is).   Discuss briefly the variables that are used in Regression #7 and Regression #9.

11.        What is the analysis of Regression #10 on page 8 and Regression #11 on page 8 called?  Be specific about where else the slope coefficient in Regression #11 is found.

12.        Some subtraction variables are generated prior to Regression #12 on page 9. They are used in Regression #12.  Use the analysis of Regression #12 to answer the following question.  From      Regression #1 on page 2, what is the predicted fare for a new route, not in the original sample, with dist = 1000, passen = 500, and bmktshr = .5?  Develop a 90 percent confidence interval for that prediction.

13.         Regression#13 on page 9 uses a different functional form from Regression #1 on page 2.  Put in  words the slope coefficient on lndist.  Regression #14 on page 10 uses the same independent      variables as Regression #3 on page 4.  Put in words the slope coefficient on dist.  Show the           calculations for the exact change.  Following Regression #15 on page 10 are some calculations.   Briefly explain those calculations and from the result identify which function fits the data better,

Regression #3 or Regression #14.

14.        Some new variables are calculated and listed on page 11 and used in Regression #16 on page 12. Put in words the first value of zfare listed (-.846) on page 11.  Put in words the coefficient on       zpassen in Regression #16.  Why is the constant essentially zero?

Data for 2017 are added to the analysis; several new variables are generated; and the data is listed on page 13

15.         Using Regression #17, Regression #18, and Regression #19 on page 14, carry out the Chow test   (SSR version) to see if the coefficients in the function estimated change between 2017 and 2020. Use a .01 level of significance.  Show your formula, fill in the formula, show some calculations      and your calculated F.  Then show this F value on a picture of the F distribution with as                  statement of the hypothesis and conclusion.

16.         Regression #20 on page 15 adds two additional variables to that of Regression #17 on page14.  Explain clearly the meaning of the constant, the coefficient on bmktshr, and the coefficients on the two new variables.

17.        Write out the model being estimated in Regression #21 on page 15.  Following that regression is a test.  State the null and alternative hypothesis for this test.  What is your conclusion?  Are the  results the same as Question 15?  Use the same level of significance as Question 15.

18.         Page 16 carries out some rearrangement of the data to prepare to carry out Regression #22 on page 16.  Discuss briefly what type of data is being constructed and how that data is used in      Regression #16.  What are the assumptions made in Regression #22.   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 #17?

Questions 19 and 20 use Appendix 2

19. Appendix 2 presents the value of Ecommerce sales as quarterly, not seasonally adjusted values in millions of U.S.$.  Also listed is the percent of overall retail sales carried out by Ecommerce    but that variable was not used.  Put in words the coefficient on the constant, Time, Q1, Q2, and Q3 from the Regression on page 2.

20.         Continuing with Appendix 2.  On page 3 is a new variable generated that is included in the         Regression on page 3.  Put into words the coefficient on Time and Q3.  Make sure that for Time and for Q3 you include two values for the impact on ECOM (Ecommerce).