Bugen1502 Business Statistics- Variable Value Assessment Answer

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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