Question

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

Team   Revenue ($mil)   Value ($mil)
Team 1   554   2806
Team 2   676   3437
Team 3   371   1333
Team 4   628   3202
Team 5   559   1852
Team 6   312   691
Team 7   342   858
Team 8   355   851
Team 9   394   869
Team 10   219   482
Team 11   258   579
Team 12   224   513
Team 13   516   414
Team 14   203   347
Team 15   156   329
Team 16   177   326
Team 17   162   307
Team 18   332   599
Team 19   411   863
Team 20   157   296

A. 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 null and alternative hypotheses ?

- The value is?

- the test statistic is ?

B. Construct a 95​% confidence interval estimate of the mean value of all soccer franchises that generate ​$300 million of annual revenue.

C. Construct a 95​% prediction interval of the value of an individual soccer franchise that generates ​$300 million of annual revenue.

Answer 1

Regression Analysis
	r²	0.744
	r	0.863
	Std. Error	512.633
	n	20
	k	1
	Dep. Var.	Value($mil)
ANOVA table
Source	SS	df	MS	F	p-value
Regression	1,37,77,935.7802	1	1,37,77,935.7802	52.43	9.84E-07
Residual	47,30,258.4198	18	2,62,792.1344
Total	1,85,08,194.2000	19
Regression output				confidence interval
variables	coefficients	std. error	t (df=18)	p-value	95% lower	95% upper
Intercept	-777.2744	276.88	-2.81	0.01	-1358.98	-195.56
Revenue($mil)	5.2097	0.7195	7.241	9.84E-07	3.6981	6.7214
Predicted values for: Value($mil)
		95% Confidence Interval	95% Prediction Interval
	Predicted	lower	upper	lower	upper	Leverage
	785.650	533.107	1,038.192	-320.564	1,891.864	0.055

A. 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 null and alternative hypotheses ?

The P-value is 0.0000

- the test statistic is 52.4290

B. Construct a 95​% confidence interval estimate of the mean value of all soccer franchises that generate ​$300 million of annual revenue.

(533.107,1038.192)

C. Construct a 95​% prediction interval of the value of an individual soccer franchise that generates ​$300 million of annual revenue.

(-320.564,1891.864)

.................................................

The given data is:

Revenue($mil)	Value($mil)
554	2806
676	3437
371	1333
628	3202
559	1852
312	691
342	858
355	851
394	869
219	482
258	579
224	513
516	414
203	347
156	329
177	326
162	307
332	599
411	863
157	296