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LIR 832: Final Examination: Fall, 2003This examination consists of two parts. The first, worth 60 points consists of five problems. Each problem is worth 15 points. You are to answer four of your choice. If you answer five, Iwill base your grade on the four with the lowest scores. The second part of the exam, worth 40points, is an analytic essay. Instructions for the essay are found in the second section of thisexamination. The examination is scheduled to last two hours.Part I: Problems: Answer all questions as completely as you are able. Partial credit on problemsis only possible if I can locate arithmetic errors in your calculations. Show your work!!!1. Which of these equations is it possible to estimate using regression techniques? Forthose for which is it possible, explain what needs to be done to make it possible and writeout the equation which will be estimated. For those for which it is not possible, explainwhy it is not possiblea. Yi = #0 + #1X1i + $2X2i + ,b. Yi = eXiiββε011++c. Yi = βββε01221XXeiiid. Yi =βεββ01212++ +XXiiie. Yi = ββ β ε011221+++XXiii2. We are interested in the effect of the presence of various benefit programs on employeeviews of their boss. We conduct an extensive survey of employees across a number offirms; employees were chosen for this survey using a two stage random procedure. Thesurvey, which went to 4,500 employees had a 95% response rate.You estimate a regression equation in which the dependent variable is a seven pointmeasure of job satisfaction and the explanatory variables include years of education,gender, whether the individual had employer sponsored health insurance, a pension planthrough their current employer, and whether the employer threw a seasonal party. Specifically, the variables are:Job Satisfaction (JSAT) a seven point scale in which 1 (Scrooge looks goodcompared with this Bozo) to 7 (this boss is a kindly demi-god of employment)Years of Education: Number of years of schooling completed. The minimumvalue of this variable is 4, the maximum is 21, the mean is14.5, the median is 12 and the standard deviation is 2.Female A dummy variable which takes on a value of 1 if therespondent is female, 0 otherwiseHealth Indicator variable, 1 = has employer provided healthinsurance, 0 = does not have.Pension Indicator variable, 1 = has employer provided pension plan,0 = does not have.Party Indicator variable, 1 = has employer has annual seasonalparty, 0 = does not have.Based on your review of the literature, you expect that all of the variables, with theexception of female, will be positively related to job satisfaction. Gender is generallyunrelated to job satisfaction.You have estimated the equation:JSAT ED Female Health Pension PartyNrrs dard error iniiiiiii=− + ++−++===812 14 1 11 5 152 3 76 04 85 15 674500 45 4022.. . . . .( . ) (. ) (. ) (. ) (. ) (. )..[tan ()]εA. Working one coefficient at a time, Interpret the impact of each factor on jobsatisfaction and perform a hypothesis test on the coefficient against a null of $= 0. For which coefficients are you able to reject the null in a 10%, 5% or 1% test?B. In large samples, it is sometimes appropriate to distinguish between the statisticalsignificance of a variable and the magnitude of its impact. Why can thisdistinction be important? Are there instances in this model in which you mightwant to make this distinction?C. A colleague of yours is puzzled by the value of the intercept. What is theinterpretation of the intercept? Why might a naive person be concerned about itsvalue in this model? Should they be concerned?D. Another colleague of yours suggests that old people are grumps and that ameasure of age must be included in the model. You do not agree but decide to goahead and enter the age variable into the model and see what happens. Age ranges from 16 to 87 with a mean of 40 and a standard deviation of 5. When youre-estimate the model with an age variable you find:Comparing these results to the prior model, is your colleague correct that ageshould be included?JSAT ED Female Health Pension Party AGENrrs dard error iniiiiiii=− + ++++−+===812 14 05 12 35 18 092 3 76 04 85 15 67 054500 50 4222.. . . . . .( . ) (. ) (. ) (. ) (. ) (. ) (. )..[tan ()]ε3. You are working in the research department of a major corporation when you hear twocolleagues discussing the use of indicator variables in regression models. As thediscussion grows more heated, one of the parties becomes sufficiently upset that she hasbegun to wave a gun around while threatening to “go postal” over the matter. Youdecide to intervene and see if you can cool things out. Before you do this, you callsecurity to let them know that they might want to look into the situationYou approach your colleagues and ask if they would explain what the dispute is about. The unarmed colleague explains that they are studying firms’ expenditures on benefits. They are building a regression model in which the amount an individual receives inbenefits from their employer is affected by their age, their time with their currentemployer, whether they are a part time employee, and their occupation.Their disagreement is how the dummy variables for occupation should be implemented. Their information allows them to classify individuals into four broad occupations:managerial/professional/sales, administrative support (clerical), service, and manual. Thefirst researcher believes that dummy variables for each of the four occupations should beentered into the model. The second believes that only the indicators for themanagerial/professional/sales, service and manual occupations should be entered, noother arrangement of these indicators will provide an accurate measure of the effect ofoccupation on benefit expenditures.You notice that security has not shown up, but that the colleague with the gun seems tobe calmer, has put it back into her purse and is very attentive. A. In order to buy time for security and possibly diffuse the situation entirely,explain to your colleagues how occupational indicators should be entered into aregression model and which, if either, of their approaches is correct. To assurethat this takes as long as necessary, make your answer as complete as possible.B. Now that your colleagues have settled down, you all retire to a nearby PC and,using MINITAB, estimate the model. The data, from a large scale nationalsurvey, reports the value of benefits and the characteristics of


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