It is early 2019, and Fearless Breweries isa household name in the pub industry in England and Wales. Fearless operates a network of pubs, restaurants, off-licenses and other outlets. After a challenging few years, in which the company was largely written off byindustry experts, the company was rebranded in 2016, and is now considered one to watch. In an effort to improve the selection of sites for Fearless pubs in the future, the company has been analysing data from its existing pubs in an attempt to understandthe main determinants of cost and revenue. The Excel file Fearless.xlscontains details of revenues for the past year (Revenue), measured in £millions, for 47 of Fearless’s pubs. The other variables relate to data currently available at head office. This includes information on management (Management) and staff quality (Staff), both on 9 point scales (with 9 being very good and 1 being very poor); a measure of local per capita annual income (LocalIncome) measured in £000s; and an index of competitor density (Competition) measured in number of pubs within 2 miles of the site. There is also a dummy variable (ModernType), indicating the type of establishment. A value of 1 for ModernType indicates that the pub has a modern or unusual theme/ambience, and a valueof 0 indicates that the pub is of a conventional type. Lastly, there is a variable (Location) that indicates the approximate location of the pub. For this variable, values of 1, 2, 3, 4 and 5 represent the midlands, north, east, south and west, respectively.
(a) Develop a regression model for revenue using the variables available. In your report, make sure to describe your modelling process, and to interpret your final model. (25marks)
(b) Described below are the details of two sites, which have been offered to Fearless. Which, if either, would you recommend the company should buy? (15marks)
Site A A rare opportunity to convert a disused church, St Candida’s, in Bournemouth, Dorset. The marketing department is wild about the idea, which has madea number of people sceptical. There are 9 pubs within 2 miles of the site, and it has been suggested that this level of competition will draw people to the site. Staffing is not thought to be a problem, although finding the right manager may be a little more difficult. Due to the presence of a reasonably high concentration of yuppies in the area, the average per capita income is relatively high at £26,500. Fixed and running costs, including rent, are thought to be around £1.75m per annum.Site BAn old family pub near Milford on Sea. The owners have run the place profitably for many years and now wish to retire. The competition density is 1 pub within 2 miles of the site, the exterior is pleasant but in need of minor repairs and re-thatching. The current members of staff
2live in the town of New Milton, and are believed to be trustworthy and loyal. Average per capita income in the area is £21,000 per annum, which is relatively low due to many of the villagers being agricultural workers. Estimated fixed and running costs, including rent, are about £1.1m.
Part 2 –Virus Testing
(a) Obtain the reported sensitivity and specificity for atest related to the COVID-19virus, andmake a reasonable assumption for prevalence. Interpret these values, and discuss the relative importance of the sensitivity and specificityfor this test. (10marks)
(b) Describe how the Prosecutor’s Fallacy could impact the interpretation of the test. (10marks)
(c) As a member of the scientific committee, Sage & Thyme, you are tasked with advising the government on the purchase of a diagnostic kit for mass testing. There are two pharmaceutical companies, CowboyInternational, who claim that their test has a positive predictive value (PPV)of 90%, and Touch Me Not Ltd., who claim aPPV of 95%. What additional information, if any, would you request from the developersto help you advise the government?(10marks)
Part 3–Blackbrier1
It is 9.30am on a Monday morning, and Pamela Landy, R&D director of Mediterranean Microcircuits, has just been approached by Noah Vosen of Blackbrier Ltd to undertake some contract work. Blackbrier need some extra design help on a switching module that Noah estimates should only take one of Pamela’s engineers 4-8 days to complete. The problem is that Blackbrier need the work done in a hurry and Noah wants a decision from Pamela by noon today. Blackbrier are certainly prepared to pay. The job would be worth £300,000 to Mediterranean Microcircuits if they could fit it in. Pamela calls into her office Jason Bourne, the only engineer she has who would be competent to undertake this work efficiently.“Well, it so happens that I have no really urgent work this week”, Jasonsaid encouragingly. “As you know, I am committed to our big laser circuit project, but at the moment, I am held up waiting for the use of one of our experimental facilities, Threadstone. I need it for a full week and have been told that either next week, or the week after, will be clear –but not both. Also, I will not know until Thursday of this week which week I can have it. They tell me it looks twice as likely to be next week as the week after. The real difficulty with this is that I must confirm on Thursday whether I will definitely take it on the Monday it is offered”.“If it does come up for you next week and you don’t take it because of this Blackbrier job, when do you think you will be offered it again?”“It will be about a month, I guess, but if I can do this Blackbrierjob in four days, we’ve no need to worry either way”, said Jason.1Acknowledgements to D.W.B. who wrote the original ca se.
3“Yes, I wish we knew more about the Blackbrierproblem. If we miss the chance of the Threadstone availability this time, a month’s delay will cost us about £450,000. Any chance of you working through next weekend if the Blackbrierjob takes more than 4 days?”“No way, Pamela, I’m sorry. I have been putting in so much overtime recently that we booked the weekend away. I couldn’t disappoint the family on this one. Look, why don’t you telephone Noah Vosen again and see if he will give us until 9am tomorrow? I could run over to Blackbrierthis afternoon and look at the problem. I could see definitely whether I could complete it this week.”Pamela thought this was a perfect solution and telephoned Noah Vosen with the idea.“Well, I don’t think I can go along with that, Pamela. I need to get started on this as quickly as possible. Send your engineer over this afternoon by all means, but unless you let me know definitely before noon, I will still telephone some other contacts. If one of them accepts unconditionally, then your engineer’s trip will be wasted, but if they all vacillate like you, maybe first thing in the morning I could still give you the job”.Pamelasaid she would ring back in an hour. She thinks the chances are about 50:50 that some other company will agree to the jobthis afternoon. Pamelais not sure what to tell Noah.She does not anticipate the prospect of any similar offers of work for her engineer in the next week or so.
(a) Draw a decision tree for the problem, andprovide advice as to what Pamela should do based on an expected value criterion. (15marks)
(b) Provide advice to Pamela based on a maximin criterion. (5marks)
(c) Investigate how the optimal course of action changes with respect to different values for:(i) the probabilitythat the Blackbrier jobwill be completed this week, and (ii) the probability that Threadstone will become availablenext week. (10 marks)