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:

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.  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.

Question 1 through 15 uses 2017 World Bank data that is listed on page 1 of Appendix 1. This data is a selection of 31 middle income countries.  Pages 7 of Appendix 1 lists data for both 2007 and 2017.       Questions 1 through 12 use just the data for 2017.  Questions 13-15  use data for both 2007 and 2017.

Regression #1 on page2 sets out to explain Life Expectancy in terms of per capita income           (Real_GDP_PC), access to sanitation, child mortality, population density and the region of the   world the county is located.  State clearly the meaning of the constant, the slope coefficient on Real_GDP_PC and the slope coefficient of LatAm.

Regression #1 continued.  Based on the p-values computed by Stata, which of the population    slopes are significantly different from zero at the .01 level of significance.  Be clear which           numbers you are comparing.  Conduct a t test for Child Mortality. State the null and alternative hypotheses; draw a picture of the probability distribution (make sure critical t value is on           picture); and show your conclusion on the picture.  What does it mean for a coefficient in          multiple regression to be significantly different from zero?

Regression #1 continued.  From the Analysis of Variance table printed, show the formula and      calculations for the R-squared and Adjusted R-squared.  Put in words the R-squared for this         problem. The results printed provide a 95% confidence interval for Sanitation_access.  Compute an 80% confidence interval.  Draw a picture of the probability distribution.

Regression #2 on page 2 uses some output from Regression #1 in the middle of page 2.  What is being tested with this regression?  What is the name of the test?  What is the conclusion with    α = .05? What is the conclusion with α = .01?

Regression #3 on page 3 has the same coefficients as Regression #1 but the standard errors have changed.   Write out the estimated function for both Regression #1 and Regression #3 with the   standard errors of the slope coefficients written appropriately under each coefficient from each regression.  Explain briefly why these new standard errors may be more appropriate (use at         least one matrix statement in your answer).

Following Regression #4 on page 3 is a prediction with a list of data for each of the countries     following at the bottom of page 3 and top of page 4.  What information and conclusion can you reach from the list of data provided?

Some new variables were generated near the middle of page 4 and used in Regression #5 on   page 4.  Using Regression #5, compute a 99 percent confidence interval for the life expectancy for a new middle income country not in the original sample which as a real gross domestic       product per capita of $9 thousand; 60% of theurban population has access to sanitation; the    child mortality rate is 30 per 1000 live births; and the country has a population density of 50    people per sq. km of land area.

Two new variables were computed at the top of page 5 and used just below in Regression #6.    Put in words the coefficient on Child_Mortality in Regression #6 using both an approximate and exact value.   Show any formulas and calculations.

Continuing with Regression #6 on page 5.  Put in words the coefficient on lnReal_GDP_PC.

10.        Some new variables are computed in the middle of page 5 and used in Regression #7 on page 5. Put in words the coefficient of Child_Mortality and put in words the coefficient of                          Child_Mortality_Africa.

11.         Below Regression #7 on page 5 is a Stata command test.  State clearly the null and alternative hypothesis being tested.  As part of the test output is an F value.  Write out the R² formula for this F statistics.  Using both Regression #4 (on page 3) and Regression #7, fill in the values for  this formula and show that the result is the same as the F value computed by Stata.

12.        Some new variables are computed and printed on page 6.  Put in words the value of                    zPop_density for Bangladesh.  Put in words the coefficient on zPop_Density in Regression #8 at the bottom of page 6.  Why is the noconstant option used?  What would be the result if the      noconstant option was not used?

13.         Using the 2007 and 2017 data that is listed on page 7, a number of new variables are computed at the top of page 8 and then listed on page 8 and top of page 9. Using Regression #9 and           Regression #10 on page 9 and Regression #11 on page 10, carry out a Chow Test (the SSR            version) to see if the coefficients on the function estimating Life Expectancy changed between

2007 and 2017.  Please show your formula, fill in the formula, calculate your test statistic and show that value on a picture of the probability distribution.

14.          For Regression #12 on page 10, state clearly (a) what the constant tells us (ie, put the constant into words); (2) what the coefficient on Y17 tells us; (3) what the coefficient on Real_GNP_PC   tells us; and (4) what the coefficient on Y17_Real_GNP_PC  tells us.

15.        The bottom of page 10 carries out some rearrangement of the data which is listed at the top of  page 11 and used in Regression #13 on page 11.   Discuss briefly what type of data are we            starting with and what type of data is being constructed and how that data is used in Regression #12.  What are the assumptions made in Regression #13.   What would be an example of              another variable that could appropriately be included as an independent variable in the analysis explaining Life_Expectancy.  How would that variable be dealt with in Regression #13?  What      assumption of OLS would be violated if that variable was correlated with one of the

independent variables used in this analysis?

Questions 16 through 20 utilize quarterly U.S. data, not seasonally adjusted, from the first quarter of    2005 to the fourth quarter of 2018 (Surplus/Deficit data ended at that point on FRED data).   This data   from the St. Louis Federal Reserve is listed on page 1 and 2 of Appendix 2 with the analysis following on subsequent pages.

The variables are:

Bond10Yr

UnemplRate

Interest on Long Term Federal Bonds with 10 year maturity (percent)

Unemployed as Percent of Work Force (Ages 16-65)

FedSurplus                       Federal Government Budget Surplus (billions $ - negative no. = deficit)

GDP                                   Gross Domestic Product (billions $)

DefGDP                             Ratio between FedSurplus and GDP (as a percent of GDP)

Q1                                      =1 if observation is for a first quarter (Jan-March)

Q2                                      =1 if observation is for a second quarter (April-June)

Q3                                      =1 if observation is for a third quarter observation (July-Sept)

Q4                                      =1 if observation if for a fourth quarter observation (Oct – Dec)

Note:  While Federal taxes are collected and paid throughout the year, April 15th  is the deadline for filing and completing the payment of taxes due from the prior calendar year.

16.         Regression #1 on page 3 of Appendix 2 sets out to explain the U.S. Government Deficit as a       share of GDP (DefGDP)  in terms of GDP, Bond10Yr, UnemplRate and the quarter in which  the  observation falls.  Put in words the constant, coefficient on UnemplRate, and the coefficient on

Q4.

17.         Regression #2 on page 3 adds some variables that were computed following Regression #1 and uses a Stata test following the regression.   What is this test called? What is it testing for? And  what is the test’s conclusion?

18.        A new variable is generated at the top of page 4 and used in Regression #3.  Compute the            predicted change in DefGDP if GDP goes from 4,000 billion to 4,001 billion.  Put that change into words.

19.         Put in words both the constant and coefficient on Time for Regression #4 and Regression #5 on page 4.

20.         Put in words the coefficient on l2.GDP from Regression #6 on page 5.  Graph the lag distribution computed with Regression #6.