LIR 832: Final Examination: Spring, 2004This examination consists of two parts. The first, worth 45 points consists of four problems eachworth 15 points. You are to answer three of your choice. If you answer four, I will base yourgrade on the three with the lowest scores. The second part of the exam, worth 55 points, is ananalytic essay. Instructions for the essay are found in the second section of this examination. The examination is scheduled to last two and one half hours.1. A friend of yours is interested in the effect of High Performance Work Systems (HPWS)on employees’ ability to return to work after an injury. It is their belief that HPWSmakes it more difficult for injured employees to return to work because there are fewerlight duty jobs suitable to a person who is not fully able to work. This suggests that (1) alower percentage of employees will be in light duty capacities in HPWS work sites thanin non-HPWS work sites and (2) employees working on HPWS sites will spend longeraway from work (have more loss time work days) when they have an accident and thanworkers in non-HPWS work sites. Your friend has an article in the “Journal ofOccupational Health and Medicine” on that very issue. Unfortunately your friend is notfamiliar with regression models and asks you to explain the statistical findings. Themodel is estimated on information from 1,000 employees in manufacturing whose work-related injury was sufficiently serious that they have at least one lost work day because ofthe injury.We expect all of the variables but facility to be positively related DAYSLOST,we expect a negative relationship between FACILITY and DAYSLOST.DAYSLOST = 3.5 + 4.2*SERIOUSNESS + 1.3*AGE + 2.1*FACILITY + 2.2*HPWS (3.4) (.53) (1.2) (1.5)r2 = .32 Sum of Squared Residuals = 101.5r231=.Degress of Freedom = 995Standard Error in ( )WhereDAYSLOST the number of days between the injury and when the employeereturned to workSERIOUSNESS A numeric rating from 0 to 2 indicating the seriousness of theinjury. 0 corresponds to the least seriousness, 2 to the most seriousness.AGE The age of the employee at the time of the injuryFACITITY A 0/1 variable indicating whether there is a staffed medicalfacility, such as a nurses station, at the work site (1 = yes)HPWS A 0/1 variable indicating whether the work site has a HPWS worksystem (1 = yes)A. Does the estimate support your friends belief that HPWS are associated withlonger time away from work. Explain your answer.B. Are the balance of the estimated coefficients consistent with our hypotheses aboutlost work time? Be sure to justify your answer using the methods of this course.2. Returning to problem 1, you have become interested in this issue and have obtained thedata set from the author. Your concern is the treatment of the serious injury variable, asyou believe that it should not be entered in its current form, but as two indicatorvariables. You define two new variables:SERIOUS1 This is equal to 1 if SERIOUS is 1, 0 otherwiseSERIOUS2 This is equal to 1 if SERIOUS is 2, 0 otherwiseYou re-estimate the model and find:DAYSLOST = 3.5 + 1.1*SERIOUS1 + 5.4*SERIOUS2 + 1.5*AGE - 1.3*FACILITY + 3.2*HPWS (1.4) (2.16) (.51) (.99)) (1.63)r2 = .41 Sum of Squared Residuals = 101r240=.Degress of Freedom = 994A. Statisticians often refer to moving from the type of measure of the seriousness ofan injury used in the first estimate to that used in the second estimate as makingthe measure more flexible. Before considering the estimates, why is dividing themeasure into two dummy variables better than having a single variable with a 0,1, 2 classification of seriousness?B Is there evidence in the estimates that it was a good idea to divide the measure ofseriousness into two dummy variables? Explain.C. We can test to determine whether the variable should have been divided using anF-test. Perform a 5% and 1% test comparing the two equations. There is onenumerator degree of freedom (hint: this problem is similar to one of the F-testsyou did in the Lazy Brown Dog problem set).3. As the newly-appointed Minister of Labor in the small African country of Zamunda, you havebeen asked by the king to analyze the relationship of your people’s income with the number ofgoats each person owns and each person’s education. Armed with the insight gained from thisclass, you are confident that you can impress the king in your first assignment. To address this,you go out and survey 1,000 Zamunda citizens, gathering their information on income, educationand goat ownership. Using Minitab, you run a regression on income and find the followingresults (standard errors in parentheses):ln(INCOME) = 6.3 + 0.12*GOATS + 0.27*EDUCATION(0.07) (0.10) r2 = .41 adjusted r2 = .39, whereINCOME Income of each individual, as measured in US DollarsGOATS The number of goats each person ownsEDUCATION Years of education A. Interpret the coefficients on each of the two variables. What do each of themmean? Test each variable to determine whether they have an impact on income –do they pass a 10%, 5%, or 1% significance test?B. Suspecting that education might not have a purely linear effect on ln(INCOME),you decide to add education2 to the model to determine whether education is, or isnot, linear. After adding the education2 to the model, you find the following(standard errors in parentheses):ln(INCOME) = 5.9 + 0.08*GOATS + 0.20*EDUCATION - 0.0042*EDUCATION2 (0.035) (0.08) (0.0020)r2 = .47 adjusted r2 = .42Should education2 be included in the model? Fully justify your answer.C. One difficulty of including the education2 variable is that calculating the marginaleffect of an additional year of education is not as straight-forward as it was in thefirst regression equation, where the king could just look at the coefficient on theeducation variable and know the answer (the king has some rudimentaryunderstanding of regression). If you decided to present the second equation, theking has mentioned that he doesn’t know how to interpret the marginal effect ofan additional year of education in a model that includes a polynomial (a squaredterm). As such, he needs things spelled out for him:As such, first present the equation the king could use to calculate the marginaleffect:marginal effect = Then, calculate the marginal effect of an