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 relatedDAYSLOST, 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.*****************************************************************************One-tailed T-test on the coefficient on HPWS:HA: βHPWS > 0HO: βHPWS < 0t = 2.2 / 1.5t = 1.4667Critical t-values:10% - 1.282 Reject Ho5% - 1.645 Do NOT reject Ho1% - 2.326 Do NOT reject Ho*****************************************************************************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.*****************************************************************************SERIOUSNESS AGE FACILITYHA: βS > 0 HA: βA > 0 HA: βF < 0HO: βS < 0HO: βA < 0HO: βF > 0t = 4.2/3.4 t = 1.3/.53 t = 2.1/1.2t = 1.235 t = 2.453 t = 1.75CRITICAL T-VALUES: 10% - 1.282 5% - 1.645 1% - 2.326SERIOUSNESS AGE FACILITY10% - Do NOT Reject Ho 10% - Reject Ho 10% - Do NOT Reject5% - Do NOT Reject Ho 5% - Reject Ho 5% - Do NOT Reject1% - Do NOT Reject Ho 1% - Reject Ho 1% - Do NOT Reject(Can not reject the null sincewe have a positivecoefficient)*****************************************************************************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. In what sense is the second equation’s measure betterthan that in the first equation?*****************************************************************************First model: The use of SERIOUSNESS constrains the model to suggest that there is an equaleffect of going from a “0" injury to a “1" injury as there is going from a “1" to a “2". Second model: The use of SERIOUS1 and SERIOUS2 allows there to be differences in theeffects of particular levels of injury, as measured against the “0" injury group. The second model is better because we would expect more serious injuries (2) to greatly affectthe number of days lost in a workplace, a jump that is not likely equal between “0" and “1"injuries. For example, in very serious injuries, individuals can stay be off work for extendedperiods, whether it be for the amputation of a limb, asbestos-based lung problems, or other majorproblems. While it is unclear what is classified as a “2", it would logically allow for such seriousproblems.*****************************************************************************B Is there evidence in the estimates that it was a good idea to divide the measure ofseriousness into two dummy variables? Explain.*****************************************************************************R-squared and Adjusted R-squared – Adjusted R-square jumped from .31 to .40 (lower SSR)Coefficient on FACILITY - Changed from positive and reasonably significant (two-tailed) tonegative, which goes along with our original theoretical conclusionsCoefficient on SERIOUS2 - Highly significant (Reject one-sided Ho at 1% level). Also showssignificant difference between it and SERIOUS1, a result we would expect (serious injuriesshould have a larger effect on DAYSLOST than minor injuries).*****************************************************************************C. We can test to determine whether the variable should have