MSCI 212 Statistical Methods for Business
Please read the following instructions carefully.
a) Your coursework must be submitted in an unsealed envelope in the coursework submission box outside LUMS A51 by 6:00 pm on Monday, 22nd January 2018.
b) Your coursework will NOT be accepted unless you sign and return a declaration form (available from the Web Board) that includes the statement that you have read and understood the University regulations relating to plagiarism. Plagiarism includes:
• Collusion, where a piece of work prepared by a group is represented as if it were the student’s own;
• The purchase of a paper from a commercial service, including Internet sites, whether pre-written or specially prepared for the student concerned;
• The submission of a paper written by any other person, including a friend, a fellow student or a person who is not a member of the university;
• The submission of another student’s work, whether with or without that other student’s knowledge or consent.
Incidents of plagiarism are recorded on a student’s file. Penalties are in line with the institutional framework of the University.
c) In accordance with University regulations, marks are deducted from any coursework which is not submitted by the deadline. This penalty will apply for 3 days after the deadline and then a mark of zero will be given to any work not submitted. However, if an extension is given then the rule applies from the date of the extension.
d) This coursework has two questions and you must answer both questions in full.
e) Both questions carry equal marks (50%) and you should be able to begin Question 1 immediately; for Question 2 some other important tools will still be covered later.
f) Each of your answers should state clearly your reasoning. Please also state clearly any assumptions that you have made in addition to those given in the questions.
g) You are allowed to submit handwritten answers but should include carefully selected extracts of your SPSS output to justify your answers. Also, please write neatly for if we cannot read your handwriting your answer will NOT be marked.
Question 1: Patient Care at NHS Hospitals in the UK
A newly appointed health minister has heard reports that there are some hospitals in England where the average length of stay of patients is over 2 weeks, whereas in many others the average length of stay is under 1 week. This sounds rather odd at face value, but he realises that he does not understand much about the activity levels of hospitals and would like to improve his level of understanding. Suppose that the SPSS data file ‘Hospital PIs.sav’ contains the following data for the 303 NHS hospitals in England:
• Hospital – Code identifying hospital;
• ALLPatients – Patients admitted in last year;
• Males – Male patients admitted in last year;
• Females – Female patients admitted in last year;
• Emergencies – Emergency patients admitted in last year;
• LOS – average length of stay of patients in last year;
• Age – average age of patients admitted last year;
• LOS PY – average length of stay of patients in previous year;
• Age PY – average age of patients admitted previous year.
Draw a sample of size 100 from this population using SPSS. As in workshop 2, use to set your unique starting point for the SPSS random number generator. Specifically, use the last four digits of your library card PLUS 1, i.e., if your library card ends ‘4321’ type in ‘4322’, and if your library card ends ‘4329’ type in ‘4330’. Record these four digits at the top of your answer.
a) In no more than 6 pages describe the main features of your sample as if to a non-statistical health minister. You should include main features of individual variables (8 marks) and of the relationships between them (8 marks). You may quote values from your SPSS output and you may include SPSS numerical and graphical output. (Both clarity and content of your report are important). (16 marks)
b) In no more than one page, without looking at the full dataset, suggest which of the patterns/features noted in your sample (of 100) you think are also likely to be true of the full population of 303 hospitals. Justify your answer as much as you can. (4 marks)
Question 2: Prediction of Car Sales at Motor Vehicle Dealerships
A chain of car dealerships sells motor vehicles and wishes to predict the monthly sales of individual dealerships. They have randomly selected 40 months’ data (see file ‘GarageChain.sav’) on Sales plus four other variables, as they think that sales may depend on some or all of the other variables:
• Sales – Sales from a dealership (£00s);
• Sellers – Number of Salespeople;
• Temp – Average temperature (◦C);
• Types – Number of different types of vehicle in stock;
• Adverts - Advertising expenditure (£).
a) Carry out a preliminary analysis of the data using Scatterplots, Correlations, and anything else you think appropriate. Report your preliminary findings. (4 marks)
b) Use multiple linear regression to investigate the relationship between sales and the four available explanatory variables. Justify your choice of model. (5 marks)
c) Carry out a residual analysis to check whether or not the usual regression assumptions seem to hold for your preferred model. Carefully justify your conclusions, noting any reservations you have about your equation. In particular, is there any evidence of high and low temperatures both discouraging sales? (4 marks)
d) In the light of your answer to (c) carry out any further improvements to your model you think appropriate (if any), and explain why you believe it is an improvement. (4 marks)
e) Suggest ‘target’ sales for a month in which the number of types of vehicle in stock is 9, there are 8 sales people, advertising has been set at £800 and the weather forecasters predict an average temperature of 14◦C. Explain the meaning of your target as if to the dealership management. (3 marks)
New Page Limit: 15 pages total (1 cover page, 6 pages for Q1 part a), 1 page for Q1 part b), 7 pages for Q2)