Methods For Decision-making And Probability Analysis

Standard Reference Lottery

1 (a) The standard reference lottery is the method of predicting probabilities of happening or not happening something in the gamble games. This method of probability prediction is mainly used for the purpose of assessing and finding out the preferences between the intermediate choices. The example of standard reference lottery is depicted in the chart given below (Sox, 1988): 

Figure 1: Example of Standard Reference Lottery (Sox, 1988)

1 (b) The marginal analysis is a managerial tool used for the long term as well as day to day decisions. The marginal analysis takes only the relevant information into account and for this reason it is considered to be most appropriate and efficient managerial tool (Armstrong, 2006). The analysis of cost and benefits is based in the additional information which reduces the burden of analyzing large data and also simplifies the decision making process apart from making it more relevant. However, there are certain disadvantages of using the marginal analysis also. For instance, the marginal analysis does not provide standard format of reporting, thus, the results of the analysis can not be used for reporting purpose. Further, overall picture of profitability is also not presented by the marginal analysis (Armstrong, 2006).       

1 (c-1) The optimist believes that the market conditions would be favorable to them and hence, it would take a view that the demand of X-120 will increase in the coming year. The highest profit is given under the alternative of new equipment of $240,000; therefore, the optimist would go for hiring new equipment.     

1 (c-2) The pessimist believes that the market conditions would be unfavorable to them and hence, it would be anticipated that the demand will decrease in the coming year. In this case, optimist would chose overtime alternative with the net profit of $100,000. However, operating at the current level will also yield the same amount of profits, but if the prediction of the pessimist does not go right i.e. if the demand increases, then overtime option will dominate the current level operations.       

1 (c-3) According to the Maximax criterion of regret, the new equipment having maximum output (net profit of $240,000) would be marked for selection.

1 (c-4)

 The expected monitory value of is highest in the case of new equipment, therefore, the preferable alternative will be hiring of new equipment. 

1 (c-5) According to the decision making theory, the expected value of the perfect information is the price that one is willing to pay to get the perfect information. Further, in computing the expected value of perfect information, the consideration can also be given to the loss that may be caused due to unavailability of the perfect information (Drury, 2008).    

Marginal Analysis

2 (a) The medical professionals should go for construction of the private clinic as the net benefits will be $120,000 as shown in the table given below:

 2 (b)    The revised probabilities are as under:

            Favourable study- favourable market =          0.90

            Favourable study- unfavourable market =      0.10

            Unfavourable study- favourable market =      0.30

            Unfavourable study- unfavourable market =  0.70

2 (c) The posterior probability of a favourable market will be 0.45 (0.50*0.90).

2 (d)

When the consultant was not engaged, the net benefits were amounting to $120,000; however, after engaging the consultant, the net benefits are estimated to be $171,000 ($176,000-5,000). Therefore, considering the increase in estimated net benefits, it could be advised that the consultant should be engaged.       

3 (a)

3 (b)

Formula View with Row and Column Headings 

3 (c)

Formula View with Row and Column Headings 

The total cost to be incurred by the company towards the healthcare claims under the assumption taken in the original model is arrived at $3,683,275. However, it is anticipated that the cost of claims could increase on monthly basis at the rate of 3% instead of 2%. The increase in claim cost would however be compensated by the simultaneous increase in the employees contribution. It is expected that the employee’s contribution will be increased from $125 to $200 per month. The total employee contribution will increase significantly to $4,700,865.04 from existing $2,938,040.65. Further, the increase in total claim is observed to be $1,756,571.40 ($8,377,886.88-$6,621,315). The increase in employee contribution has been more than the increase in total claims. Resultantly, the company cost has gone down from $3,683,274.83 to $3,677,021.84.       

4 (a) Results of Regression of Wages against Score:

 Results of Regression of Wages against years of experience

 Results of Regression of Wages against score and years of experience

Cost Equation for Regressions Presented above:

In the first regression, the dependent variable wages has been tested against the independent variable score. The results of this regression depicts that the intercept (a) is 176.40 while beta (b) for independent variable (score) is 25.64 and standard error is 73.45. Further, the second regression has been conducted with the dependent variable wages and independent variable number of years. The results of this regression show that the intercept is 870.10, beta is 54.69, and standard error is 131.92. Further, the third regression has been conducted with the dependent variable wages and independent variables such as score and years. The results of this analysis show that intercept is 170.10, beta for variable-1 (score) is 24 and beta for variable-2 (years) is 38.40 and standard error is 57.22. It could be observed that the standard error is lowest in case the third case which shows that these results are the most reliable. Further, the R squared has been observed to be 0.76, 0.22, and 0.86 in the case-1, 2, and 3 respectively. The highest R square in the case-3 again shows that the results of Multiple Variable regression are the most reliable (Albright, Winston, & Zappe, 2010).     

The Multiple Variable regression is improvement over the single variable regression model (Woolson & Clarke, 2011). The Multiple Variable regression model takes two or more factors into account while conducting regression analysis. Since, multiple factors are taken into consideration, therefore, this model is considered superior for use in the estimations and predictions (Woolson & Clarke, 2011).  

4 (b) In case the results of single regression are used, it would be preferable to use regression of wages against score. The R squared of this regression is 0.76, higher than the R squared of regression of wages with years of experience of 0.22. The R squared explains the proximity of the data of independent and dependent variable. In other words, it explains how closely the outcome of dependent variable is linked to the independent variable (Elliott & Woodwar, 2014).      

4 (c) The intercept of Multiple Variable regression is 170.10, which is lower than the intercepts of the single variable regressions. Further, the Multiple Variable regression provides two beta values that is one for each independent variable. The beta values computed in the Multiple Variable regression are lower than the beta values computed individually for both the independent variables. In Multiple Variable regression, the beta value for independent variable-1 is 24 and for the independent variable-2 it is 38.40. However, the beta values in case of individual regressions have been observed to be 25.64 for variable-1 and 54.69 for variable-2.    

4 (d)

 As per the Multiple Variable regression, the wages of the trainee who scores 30 and possesses 2 years of experience will be $1,024.   

5 (a)

 5 (b)

 5 (c)

 5 (d-i)

 5 (d-ii)

References

Albright, S.C., Winston, W., & Zappe, C. 2010. Data Analysis and Decision Making. Cengage Learning.

Armstrong, M. 2006. A Handbook of Management Techniques: A Comprehensive Guide to Achieving Managerial Excellence & Improved Decision Making. Kogan Page Publishers.

Drury, C. 2008. Management and Cost Accounting. Cengage Learning EMEA.

Elliott, A.C., & Woodwar, W.A. 2014. IBM SPSS by Example: A Practical Guide to Statistical Data Analysis. SAGE Publications.

Sox, H.C. 1988. Medical Decision Making. ACP Press.

Woolson, R.F. & Clarke, W.R. 2011. Statistical Methods for the Analysis of Biomedical Data. John Wiley & Sons.

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