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90-760: Decision & Risk Modeling Midterm Solution, AM Section Spring 2016Question #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?” Solution:a) This experiment illustrated the power of “anchoring” [or anchoring and (insufficient) adjustment]inasmuch as the bids turned out to be positively correlated with the last two digits of the socialsecurity number. There is no logical reason why that should be the case, but just seeing a large (orsmall) two digit number swayed the bids up (or down).b) This illustrates the cognitive bias of “over-confidence” in the sense that the confidence intervals weresystematically too narrow and, hence, too likely to exclude the true value. If class members werewell-calibrated then the true value would have turned out to fall within the 90% CI’s about 90% ofthe time.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?Solution:a) One optimizes (e.g., with Excel’s Solver) to minimize a measure of error (such as the RMSE) betweenthe model’s “backcast” for past periods and the actual observations’ values, treating the weights asdecision variables (or “blue cells”) in that optimization. [Typically would constrain the weights to benon-negative and sum to 1.0, but those additional points are not needed to get full credit.]b) Increasing the number of terms (or, equivalently the number of degrees of freedom) will improve thefit to past data but – when carried too far – can jeopardize the fit to the future data on is trying topredict because of overfitting.c) You’d expect w2 > w5.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? Solution:a)b) 3 (Note: Group #3 since it has the most experience and highest GPA.) c) None. The centroids would have had five-coordinates, not just two, but that would have just filled in cellsD3:F6. The number of columns in the rest of the display is governed by the number of groups, not thenumber of predictors.d) 22.66Question #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? Solution:a) GPA and years of experience, respectively.b) B, D, A, C, respectively.c) The coordinates are given in the previous question. They are (3.19, 2.80).d) Group 1Question #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.) ______________________________________________ Solution:a) =SUMPRODUCT(B$2:F$2,B4:F4)b) =SUMPRODUCT(B$2:F$2,B4:F4,B4:F4)-H4^2c) =SQRT(I4)d) =J4/H4e) Smiley face goes in the lower right cornerf) #2, #3, and #7Question #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) What 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 ASolution:a) Normal and uniform, respectively.b) $20.83 - $70.38c) $47.53 +/- 1.65 * $10.08 / SQRT(10,000) = $47.37 - $47.70d) Option B has a 30% chance of producing an outcome of 40 or

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