Question
The Australian Football League (AFL) currently has 18 teams based in the various Australian States, Victoria, NSW, South Australia, Western Australia and Queensland. These teams play a unique Australian football code, Australian Rules football, and the season consists of 24 rounds. Football is an increasingly competitive and professional business in Australia and the budgets for the clubs reflect this. There has long been a feeling that better resourced and more popular clubs have an advantage with their larger expenditure leading to greater success on the field. The data provided give the amount spent by the Football Departments of the AFL clubs from 2003 to 2007 as well as their results (Source: The Australian newspaper, 13 March 2008). There are three variables:
Club: The name of the AFL club
Spent: Total football expenditure, in millions of Australian Dollars Wins: The total number of wins from 2003 to 2007
All tables, graphs and comments for this question should be placed in the appropriately labelled spaces in the worksheet Results.
(a) Which is the independent (or predictor) variable and which is the dependent (or response) variable in this case? Give reasons for your choice and answer in Textbox (a)
(b) Produce a scatter plot of the data (Graph (b)). The chart must have appropriate title and labels. Also you should rescale the graph axes to most clearly display the data. Based on the scatter plot, describe the type and direction of relationship between the variables. Is the relationship deterministic or probabilistic? Answer in Textbox (b).
(c) Using the regression function in Excel, generate regression output for the data and place it where indicated in the Results worksheet.
i. Write down the line of best fit for the given data from the regression output obtained. Explain the meaning of any symbols used. (Textbox (c))
ii. State the value of the slope of the equation correct to three decimal places and give an economic interpretation of this value in Textbox (c).
iii. State the value of the intercept of the equation correct to three decimal places and give an interpretation of this value in Textbox (c). Does the intercept value represent a practical value in this case? Explain briefly.
(d) Do the data provide statistical evidence of a linear relationship between the amount spent by the football department and the number of wins for the team? Perform an appropriate hypothesis test using the p-value method. Answer in Textbox (d).
i. State null and alternative hypotheses. (You are not required to type Greek letters with subscripts. You may use words or symbols instead of Greek letters. For example, Ho can be written as H_0, and β1 as beta_1, etc.)
ii. State the appropriate p-value for this test from the regression output. If the significance level were 5%, would the null hypothesis be rejected? At what levels of significance will the null hypothesis be rejected?
iii. Is there are statistically significant relationship between amount spent by the football department and the number of wins for the team? State your conclusion with reference to your decision about the hypotheses.
(e) State the coefficient of determination from the regression output to three decimal places. How good a fit is this linear model to the data? Answer in Textbox (e)
(f) Predict the sales the number of wins (as a whole number) for a club whose football department spent:
i. 62 million dollars
ii. 70 million dollars
Comment on the reliability of each prediction. Answer in Textbox (f).
8 marks Presentation: 5 marks (If your presentation is easy to read, you will get these 5 marks. Ease of reading is assisted by appropriate font size, borders, colour choice and labelling in graphs, and some care in spelling, grammar and punctuation. )
Attachment:- 1.xls