Bài tập phân tích thống kê định I) Topic: ANALYSIS FOR DECISION MAKING One of the investments of Philip Mahn will fall due soon, he is now considering how to invest the return worth 30,000$ He is considering two investment schemes: entrusting such amount of money to a mutual fund that invests in securities (MF) or investing in a certificate of deposit with the term of one-year (CD) The certificate of deposit ensures payment of interest at 8% The estimated return on an investment in a mutual fund is 16%, 9%, and -2%, respectively depending on good, average or bad market conditions The probability of the market under good, average or bad market conditions is estimated at 0.1, 0.85, and 0.05, respectively a Please build a result-based matrix for this question b Which investment scheme will be chosen according to maximax criteria? c Which investment scheme will be chosen according to maximin criteria? d Which investment scheme will be chosen according to the criteria of lowest regret? e Which investment scheme will be chosen according to EMV criteria? f Which investment scheme will be chosen according to EOL criteria? g How much will Philip be prepared to pay so as to obtain totally accurate market forecast? REGRESSION The personnel director of a small manufacture company has collected data on salary (Y) earned by machinists working for the company together with information on average performance (X1) over the three-year period, length of services (years - X2), and the number of machines assigned (X3) (file dat9-19.xls) He wishes to build a regression model to produce an estimate of average salary that each employee may expect to receive according to the level of work completion, length of service (years), and the number of machines assigned a Please draw scatter diagrams showing the relationship between salary and independent variables Which type of relationship does each diagram suggest for you? b If the personnel director wishes to build a regression model using only one independent variable to estimate salary, which independent variable should be used? c If the personnel director wishes to set up a regression model only using two independent variables to estimate salary, which independent variables should be used? d Please compare Adjusted R2 indicator produced in question b and question c with such indicator produced by the model with all of the three independent variables Which model will you recommend this director to use? e Suppose the director wishes to use a regression model with all of the three independent variables, what is the regression equation? II) Answers: ANALYSIS FOR DECISION MAKING: a Building a LP model: With an amount of 30,000$ invested in a mutual fund (MF) and certificate of deposit with the term of one year (CD) that bears an annual interest of 8%, and return on investment in a MF at 16%, 9% and -2% depending on good, average and bad conditions of the securities market, with the respective probabilities of 0., 0.85 and 0.5 We have returns on investments in a MF, CD and both of max MV & CD correspondent with the market conditions as follows: The return on investment of MF:  Good = 30 000$ x 16% = 4800 $  Average = = 30 000$ x 9% = 2700 $  Bad = = 30 000$ x (2)% = - 600$ The return on investment of MF:  Good = 30 000$ x 8% = 2400  Average = 30 000$ x 8% = 2400  Bad = 30 000$ x 8% = 2400 The Max return on investment of both MF & CD:  Max good(MF,MD) = Max(4800,2400) = 4800  Max average(MF,MD) = Max(2700,2400) = 2700  Max bad(MF,MD) = Max((600),2400) = 2400 We have investment pay off matrix as follows: b Which investment scheme will be chosen according to maximax criteria : Status nature Description MF CD Max(State of Nature) Investment Probability MF r(%) CD r(%) Good Average Bad 4,800 2,400 4,800 30,000 0.10 0.16 0.08 2,700 2,400 2,700 (600) 2,400 2,400 0.85 0.09 0.08 0.05 (0.02) 0.08 Decision Analysis following principles of Maximax 4,800 2,400 4,800  MAX MF = MAX MF(Good, Average, Bad) = MAX MF(4800,2700,(600) = 4800  MAX CD = MAX CD(Good, Average, Bad) = MAX CD(2400, 2400, 2400) = 2400  MAX (MF,CD) = MAX(4800,2400) = 4800 According to this criteria, Philip Mahn will invest in a MF This investment produces a high gain if he makes an accurate estimate, conversely, if he makes a wrong estimate, he will make substantial loss (under good market conditions, he will earn a profit of 4,800$ Conversely, under bad market conditions, this investment will incur a loss of 600$) Conclusion: MF Investment scheme will be chosen according to maximax criteria c Which investment scheme will be chosen according to maximin criteria: Status nature Description MF CD Max(State of Nature) Investment Probability MF r(%) CD r(%) Good Average Bad 4,800 2,400 4,800 30,000 0.10 0.16 0.08 2,700 2,400 2,700 (600) 2,400 2,400 0.85 0.09 0.08 0.05 (0.02) 0.08 Decision Analysis following principles of Maximin (600) 2,400 2,400  MIN MF = MIN MF(Good, Average, Bad) = MIN MF(4800,2700,(600)) = (600)  MIN CD = MIN CD(Good, Average, Bad) = MIN CD(2400, 2400, 2400) = 2400  MAX (MF,CD) = MAX((600),2400) = 2400 According to this criteria, Philip Mahn will invest in CD, this investment is relatively safer although it produces a lower profit as compared to maximax criteria (2,400