90-760: Decision & Risk Modeling, MORNING SECTION Midterm, Spring 2016Do not turn the page until you are told to do so. Write your answers below each question.Note how much each problem is worth and budget your time. Total points possible: 110Name: ______________________________Q1: _________ out of 10 possible pointsQ2: _________ out of 15 possible pointsQ3: _________ out of 20 possible pointsQ4: _________ out of 20 possible pointsQ5: _________ out of 25 possible pointsQ6: _________ out of 20 possible pointsTotal Possible Points: 110Question #1: (10 points)State the name of the associated cognitive bias or concept and then also concisely explain the key ideasunderlying these points from the first class, using neat handwriting. (Verbose or illegible answers will not begraded or will be marked down sharply.)a) Ariely et al.’s experiment with Sloan School MBA students being asked to bid on objects after writingdown the last two digits of their social security numbers.b) Only about half of the class’ 90% confidence intervals contained the correct answer when trying toanswer questions like “In what year did Berners-Lee coin the term World Wide Web?” Question #2: (15 points)For the weighted moving average time-series forecasting method, concisely answer the following in neathandwriting. (Verbose or illegible answers will not be graded or will be marked down sharply.)a) How does one find the weights?b) How does increasing the number of data points included in the average affect the model’s fit to historicaland future data?c) If “all is well” (data are stationary, the method is working as it should, etc.) what would you expect to bethe relative magnitude of the weights on the 2nd and 5th most recent data points? Question #3: (20 points)I ran discriminant analysis with the DA.xla add-in on a data set concerning job applicants and obtained theresults shown below, with some cells deleted.a) Fill in the 8 missing cells in the confusion matrix & also the % correct for the training sample.b) How many of the classification sample observations are predicted to be in the strongest group?c) How many more columns would I have had to display for this problem if there had been five predictorvariables?d) How far is Observation #5 in the classification sample from the centroid for group #1? Question #4: (20 points)Below I show the data from the previous problem in both a table and a scatter plot. a) What are the labels on the horizontal and vertical axes of the scatter plot?b) Identify by letter (A through D) which group is which.Training Data Group #1: __________Training Data Group #2: __________Training Data Group #3: __________Classification Sample: __________c) Mark with a star on the graph where the centroid for Group 2 is. (Take your time and be precise. Youshould be able to place it within 0.2 on each dimension.)d) According to the 3-nearest neighbor rule, to what group does an applicant with a GPA of 2.5 and twoand a half years work experience belong? Question #5: (25 points)Below is a screen shot of a payoff matrix with 10 alternatives and 5 states of nature and its associated risk-return frontier, plotting standard deviation vs. expected value. Assume big numbers are good.a) What is the formula in Cell H4? __________________________________________b) What is the formula in Cell I4? __________________________________________c) What is the formula in Cell J4? __________________________________________d) What is the formula in Cell K4? __________________________________________e) Draw a smiley face in the most desirable corner of the risk-return frontier.f) Which option(s) is/are not on this frontier? (Identify them by number.) ______________________________________________ Question #6: (20 points)I have pasted below the result of a Monte Carlo simulation with 10,000 trials comparing two options, A and B,including their cumulative risk profiles. You may assume that big numbers are good.a) Which random variables do the results of Options A and B resemble? (Just give the overall name; don’tworry about trying to specify the parameter values.)b) What is a 90% confidence interval for the result with Option A?c) What is a 90% confidence interval for the expected value of Option B?d) What is the interpretation of the cumulative risk profile for Option B passing through the point (40, 0.3)?e) Circle all of the following statements that are true.Option A statewise dominates Option B Option B statewise dominates Option AOption A 1st order stochastic dominates Option B Option B 1st order stochastic dominates Option AOption A 2nd order stochastic dominates Option B Option B 2nd order stochastic dominates Option
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