Question

Can annual sports team revenues be used to predict franchise​ values?

Team   Revenue ($mil)   Value ($mil)
Team 1   552   2815
Team 2   677   3436
Team 3   372   1329
Team 4   625   3198
Team 5   557   1847
Team 6   313   691
Team 7   339   856
Team 8   354   849
Team 9   396   867
Team 10   219   483
Team 11   257   581
Team 12   225   514
Team 13   516   415
Team 14   203   348
Team 15   154   328
Team 16   176   327
Team 17   161   308
Team 18   333   599
Team 19   413   864
Team 20   156   296

A. Predict the mean value of a soccer franchise that generates ​$250 million of annual revenue.

B. Compute the coefficient of​ determination, r2​, and interpret its meaning.

C. At the 0.05 level of​ significance, is there evidence of a linear relationship between the annual revenues generated and the value of a soccer​ franchise?

- the test statistic is ?

D. Construct a 95​% confidence interval estimate of the mean value of all soccer franchises that generate ​$250 million of annual revenue.

E. Construct a 95​% prediction interval of the value of an individual soccer franchise that generates ​$250 million of annual revenue.

Answer 1

(a) Mean value = 528.134771

(b) r2 = 0.741

74.1% of the variation in the model is explained.

(c) The hypothesis being tested is:

H₀: β₁ = 0

H₁: β₁ ≠ 0

t = 7.179

The p-value is 0.000.

Since the p-value (0.000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the model is significant.

(d) The 95​% confidence interval estimate of the mean value of all soccer franchises that generate ​$250 million of annual revenue is between 242.072 and 814.197.

(e) The 95​% prediction interval of the value of an individual soccer franchise that generates ​$250 million of annual revenue is between -592.711 and 1648.981.

The output is:

	r²	0.741
	r	0.861
	Std. Error	515.834
	n	20
	k	1
	Dep. Var.	Value
ANOVA table
Source	SS	df	MS	F	p-value
Regression	1,37,11,803.4612	1	1,37,11,803.4612	51.53	1.11E-06
Residual	47,89,523.4888	18	2,66,084.6383
Total	1,85,01,326.9500	19
Regression output				confidence interval
variables	coefficients	std. error	t (df=18)	p-value	95% lower	95% upper
Intercept	-771.7031
Revenue	5.1994	0.7243	7.179	1.11E-06	3.6777	6.7210
Predicted values for: Value
		95% Confidence Interval	95% Prediction Interval
Revenue	Predicted	lower	upper	lower	upper	Leverage
250	528.135	242.072	814.197	-592.711	1,648.981	0.070