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. Assuming a linear​ relationship, use the​ least-squares method to compute the regression coefficients b0 and b1.

B. Predict the mean value of a soccer franchise that generates ​$200 million of annual revenue.

Answer 1

	Revenue (x)	Value (y)	x2	y2	xy
	552	2815	304704	7924225	1553880
	677	3436	458329	11806096	2326172
	372	1329	138384	1766241	494388
	625	3198	390625	10227204	1998750
	557	1847	310249	3411409	1028779
	313	691	97969	477481	216283
	339	856	114921	732736	290184
	354	849	125316	720801	300546
	396	867	1940497	751689	343332
	219	483	3576290	233289	105777
	257	581	6694251	337561	149317
	225	514	13250118	264196	115650
	516	415	26109611	172225	214140
	203	348	51908973	121104	70644
	154	328	103719977	107584	50512
	176	327	207325033	106929	57552
	161	308	414524750	94864	49588
	333	599	827109003	358801	199467
	413	864	1650641716	746496	356832
	156	296	3294589181	87616	46176
Total	Σx = 6998	Σy = 20951	Σx2 = 6603329897	Σy2 = 40448547	Σxy = 9967969

A. Least squre method: y = b₀ + b₁x

b₁ = (nΣxy − ΣxΣy)/(nΣx² − (Σx)²) = (20*9967969-6998*20951)/(20*6603329897-6998*6998) = 0.0004

b₀ = (Σy − m Σx)/n = (20951-0.004*6998)/20 = 1046.15

y = 1046.15 + 0.0004x

B. Revenue: x = $200 million

Franchise value ($ million): y = 1046.15 + 0.0004x = 1046.15 + 0.0004*200 = 1046.15+0.08 = 1046.23