BUGEN1502 Business Statistics- Variable Value
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:
(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.
(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.
Answer:
The details of dependent variable and independent variables are highlighted below: Dependent variable: Number of wins that the team registers Independent variable: Money Spent Reasons: It can be said that as the money spent on the development of team increases, the performance of the team member would also be improved. Further, number of wins which have been registered by the team is mainly the measure of team performance. Therefore mon
ey spent is the independent variable and number of wins that a team registers is the dependent variable.
ey spent is the independent variable and number of wins that a team registers is the dependent variable.
It can be seen from the scatter plot that the nature of the association between money spent and number of wins register is probabilistic. This is because the output would vary with respect to the random sample collected from different club or with same club. This indicates that similar type of relationship would be incurred on the repetitive data. However, the actual intensity of the positive association would not be same and would be dependent on the underlying data. Hence, it would be fair to conclude that the data variables are not showing any specific or say fixed relationship because the number of wins registered by the team is probabilistic event. Thus, only a general tredn can be obtained.
The line of best fit for the regression model is highlighted below: Number of wins registered by team = -13.574 + (1.168* Money spent) Where, Slope coefficient (Money spent) = 1.168 Intercept = −13.574 (ii) The value of slope coefficient i.e. 1.168 indicates that when the money spent on the team is increased by a sum amount of AUD 1 million, then the number of team wins would increase by 1.168 units (on an average). (iii) The value of intercept i.e. -13.574 indicates that when the money spent on the team is zero, then the number of team win on an average would be -13.574. However, number of wins as decimal or negative is not a realistic case because the team win must be either zero or positive and also be an integer value.
Hypotheses are furnished below. H_0 (Null Hypothesis): Beta_1 = 0 H_1 (Alternative Hypothesis): Beta _1 ≠ 0 (ii) It can be seen from the regression output that the p value for the slope coefficient is 0.091. Significance level = 5% It is apparent that p value is higher than the significance level (0.091 >0.05) and thus, insufficient evidence present to reject the null hypothesis and to accept the alternative hypothesis. Further, null hypothesis would only be rejected when the significance level is higher than 9.10%. (iii) From the above, it can be said that alternative hypothesis would not be accepted and hence, the claim furnished in the null hypothesis is correct. Therefore, it would be fair to conclude that there is no statistically significant relationship that exists between amount spent by the football department and the number of wins for the team.
Based on the regression analysis, the value of coefficient of determination (R square) comes out to be 0.190. The value of coefficient of determination indicates that 19% of the variation in the dependent variable (Money spent) would be explained by the variation in the independent variable (number of wins registered by team). This is significantly low percentage and thus, independent variable does not explain the large proportion of changes in the dependent variable. Hence, the regression model is not a good fit for the analysis.
The regression line is highlighted below: Number of wins registered by team = -13.574 + (1.168* Money spent) (i) Money spent: 62 million dollars Number of wins registered by team = -13.574 + (1.168* 62) = 59 It can be said that independent variable value falls within the range which has been utilised for computation of regression line. Hence, this prediction is reliable. (ii) Money spent: 70 million dollars Number of wins registered by team = -13.574 + (1.168* 70) = 68 It can be said that independent variable value does not fall within the range which has been utilised for computation of regression line. Hence, this prediction is not reliable.
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