Problem 1: As at workshop 2, use Transform Random Number Generators to set your unique starting point for the SPSS random number generator. For this coursework question 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 government think-tank is interested to understand the compensation payments to CEOs that have occurred over the last month. Suppose that the SPSS data ?le 'ExecutiveCompensation.sav' contains: Salary (000), Name, Industry and Total Compensation (000000) of the 1501 CEOs who have been paid off in the last month.
Draw a sample of size 100 from this population and investigate your sample using SPSS.
a) In no more than 6 pages describe the main features of your sample as if to a non-statistical civil servant working for the think-tank. You should include main features of individual variables and of the relationships between them. You may include SPSS numerical and graphical output and/or you may quote values from your SPSS output. (The clarity and content of your report are both important).
b) Without looking at the full dataset, suggest which of the patterns/features noted in this sample (of 100) you think are also likely to be true of the full population of 1501 CEOs. Justify your answer as far as you are able.
Problem 2: You should include key parts of your SPSS output in your answer. You must explain your answer clearly and you are limited to a maximum of 6 pages.
A cross-channel ferry company is interested in predicting the amount of duty-free goods (e.g. wines, spirits, beer, cigarettes, and perfumes) that it can expect to sell to passengers as they cross the channel. Sales are believed to depend, to some extent, on passenger numbers and the company therefore wishes to use information on passenger numbers to predict likely sales values.
Data has been collected for 100 crossings, recording the value of sales of duty-free (£'s), the total numbers of passengers, the numbers of adult passengers and the number of child passengers. The data is stored in columns 1 to 4 of the data file 'ferysal2.sav'.
a) Plot graphs that you think shed some light on the ferry company's idea and comment on your results.
b) Use linear regression to determine which, if any, of the total numbers of passengers, or the numbers of adult passengers or the number of child passengers show evidence of a significant linear relationship between sales and the explanatory variable? Justify your answer.
c) Which of the three models do you think is best? Justify your answer. Carry out a common-sense based examination of the residuals for your chosen model and comment on your findings.
d) Use your preferred model from part (c) to estimate the value of sales for (i) a crossing with 400 passengers in total, made up of 300 adults and 100 children; (ii) a crossing with 800 passengers in total, made up of 500 adults and 300 children. Explain your beliefs about the accuracy of your estimates as if to a manager of the ferry company.
e) Investigate as far as you are able the possibility of a multiple linear regression model using both adults and children as explanatory variables. Explain clearly what you believe your results are telling you.
f) One of the more thoughtful of the ferry company managers is worried about the regression model of sales against number of children. It seems to imply that each child on the ferry will spend, on average, about £9 on duty-free goods. However children are not allowed to buy duty-free goods! Whether or not you have recommended this model, the manager is starting to lose faith in the idea of using regression models, given that they seem to be capable of producing nonsensical results. Explain, as if to the manager, why this model seems to be providing apparently silly results.
Need problem 2 answer - You should include key parts of your SPSS output in your answer. You must explain your answer clearly and you are limited to a maximum of 6 pages.
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