Study Programme: ENTERPRISE RISK MANAGEMENTModule: ADVANCED QUANTITATIVE METHODS FOR MANAGERS ANDDECISION MAKING (ERM502)Academic Year: 2020-20214th Written Assignment (WA4)Subject 1 (25%)Workers at a Research Laboratory have raised two complains regarding their salaries.Female workers claim that male workers with the same qualifications receive highersalaries. Workers with Ph.D. qualification claim that their salaries are at the samelevel as the ones for workers without a doctoral degree. The management of theOrganization rejected both claims based on the results of a regression analysis, madeby the company’s department of statistics, on the payroll data (file Payroll.xls) for the100 employees of the Organization. Regression analysis results are as follows: ANOVAdf5SS1.5636E+10MS3127260664F344.0367Significance FRegression8.8445E-59Residual948544511139089905.45Total991.6491E+10CoefficientsStandard Errot StatP-valueLower 95%Upper 95%Intercept-5916.1893140.847-1.8840.063-12152.415320.036Years1021.69648.92620.8830.000924.5531118.839Evaluation3728.939619.8226.0160.0002498.2684959.610Articles439.14880.6935.4420.000278.931599.365Gender1089.720631.9801.7240.088-165.0902344.530PhD725.748961.5240.7550.452-1183.3802634.876 *Gender: 1= male, 0= female Ph.d: 1= Ph.D holder, 0= NonPh.Di. Is the management’s view justified based on the results of the regressionanalysis? (5%).However, female employees presented a diagram showing salaries of male and femaleemployees against years of experience, which according to them shows a differentgrowth of salaries over years of experience. ii.Reproduce the above diagram from the data in the file Payroll.xls. What doyou observe? (5%)State a regression model that includes as explanatory variables: Years,Evaluation score, Number of Articles and the interaction between Gender andiii. Years of Experience, and perform the regression based on the empirical data.Do the results justify the claim of the female employees? (5%)iv. Interpret the significant coefficients of this model. (5%)v. Comment on the significance and the explanatory power of the model and thevalidity of the Linear Regression assumptions, specifically about normality ofresiduals and presence of heteroscedasticity. (5%) vi.Write the regression equations for male and female employees derived fromthe regression model in (iii.). (5%) Subject 2 (15%)The machines on a given shop floor are of 3 types. The machines were acquired atdifferent times so their age varies. The data in the file Machine Repairs.xls containthe recorded annual Cost of repairs, Age and Type for each machine.i. Develop a regression model for the Cost, using as explanatory variables theAge and the Type of machine. Consider the interaction between Age and Typeof machine as well. (6%) ii.Perform the regression analysis and comment on the significance of the modeland the explanatory variables. (6%)Excluding all variables that you consider non-significant, run the model againand interpret the coefficients. (6%)Based on the previous results, present the regression equations for eachmachine and the relevant data on one graph. (6%)iii.iv. Subject 3 (15%)The file Manufacturing Process.xls contains sample data regarding the achievedstrength of certain metallic pieces that are reworked in a manufacturing process, alongwith the associated processing time, furnace temperature and pressure applied in eachcase.i. Develop a regression model for the achieved Strength, using as explanatoryvariables the Time, Temperature and Pressure and the Temperature –Pressure interaction. (6%) ii.Explain the coefficient of the interaction term providing some illustrativenumerical examples. (6%)Show graphically the effect of Temperature on Strength at two different levelsof pressure and explain the graph. (6%)iii. Subject 4 (15%)The data in the file FinPortfolios.xls contain the company’s portfolio performancedata. Each observation includes the average return of the portfolio, the portfoliomanager’s Age and Tenure (years in the company) as well their SAT score andwhether they are MBA graduates (Yes:0, No:1). The total assets of each portfolio inthousands of dollars is also given.The management of the financial company would like to determine to what extend allthose characteristics explain the variation among the returns of individual portfolios.A regression using Age, Tenure, MBA, SAT and Assets as explanatory variables wassuggested by the management. However the Business Analytics group suggests thatusing the logarithm of the assets [log(Assets)] is more appropriate and is used as astandard practice in industry. i.Produce two separate charts showing the % return against assets and % returnagainst log(assets) and comment and the differences. Which variable wouldyou think is more appropriate for a regression model and why? (4%)Define the two regression models as they are described above and perform theii. corresponding regression analysis. Compare the results and justify why themodel suggested by the Business Analytics group is the most appropriate.(8%) iii.Interpret the coefficients in the regression model of the Business Analyticsgroup (8%) Subject 5 (10%)A regression model for predicting demand (D) for cocoa (in million of pounds)included the following variables: P: Price of coco ($ per pound), PCInc: per capitaincome (in $) and Y: year. The estimated model is:logD = -56.665 – 0.222logP – 0.572log(PCInc) + 0.036Y (12.766) (0.034)log is the natural logarithm.(0.353)(0.006) The number in parenthesis are the standard errors of the coefficients.T-critical = 1.98Give the interpretation of the significant coefficients of the model in contextSubject 6 (20%)The Athletic Betting Company uses logistic regression models to predict the odds ofpossible outcomes of athletic games in order to set the betting payouts. For theupcoming game between two of the leading teams Pantheoi and Olympians, a logisticregression model with the response variable Y, being whether or not Panthei win(Y=1 if the win, and 0 if they lose). The predictors are:PanWin% = the percent of the previous 10 games that Pantheoi had won into thegame in question (measured from 0 to 100)OppWin% = same definition for the opponent team Home =0/1 variable corresponding a home game (1) or away (0)Temperature = the temperature at which the game was playedNational =a dummy variable showing if the game was at National League (0) orEuropean League (1). The logistic regression output is given below.ChiSquare p-value < 0.001Coefficient SE Z p-valueConstant -25.30 10.54 -2.40 0.0163PanWin% 0.466 0.176 2.65 0.0082OppWin% -0.170 0.643 -2.65 0.0081Home 1.45 0.660 2.20 0.0278Temperature 0.115 0.045 2.55 0.0108National -0.245 1.890 -0.13 0.8969i. Is there evidence that at least one of the variables is a statistically significantpredictor of whether the Pantheoi win?ii. What does the coefficient for Temperature tell you about the relationship betweenTemperature and the probability that Pantheoi win? Compute the correspondingodds ratio for a 10 degree increase in temperature and explain what it means. Givea confidence interval for this odd ratio.iii. Find a confidence interval for the coefficient of the Home variable and give abrief interpretation. Also find the odds ratio for the corresponding variable and a95% confidence interval and interpret those results.
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