# Decision Theory quiz - state of nature decision -regression analysis

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Decision Theory Second Quiz Answer all of the following questions. Equal credit (50 points each) for each Roman numeral question. I. A payoff table is given as d1 d2 d3 a. b. c. d. e. f. s1 250 600 400 s2 450 -250 500 s3 900 700 600 What choice should be made by the optimistic decision-maker? What choice should be made by the conservative decision-maker? What decision should be made under minimax regret? If the probabilities of s1, s2, and s3 are .3 .5, and .2, respectively, then what choice should be made under expected value? What choice should be made using the LaPlace method of expected value (each state of nature is equally likely)? What choice should be made using the Hurwicz method, in which the coefficient of optimism is .7? (hint: in this method, only the most favorable and least favorable states of nature are used) II.. Bus and subway ridership during the Summer is believed to be heavily tied to the number of tourists. During the past five years, the following data have been obtain Year 2012 2013 2014 2015 2016 Tourists (in millions) 12.5 12.7 13.9 15.3 16.8 Riders (100,000s) 8.5 9 10 11 12 Using regression analysis, determine the forecasted number of riders for the Summer of 2017 if 17.0 million tourists are expected during that period?

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