Question

Square footage (thousands)	Price of house thousands
2.7	478
2.3	328
2.3	309
1.8	298
1.9	303
2.1	466
1.4	328
1.6	385
2.1	360
2.9	374
2.2	387
2.6	452
2.1	462
1.8	436
1.9	424
0.95	308
1.3	430
1.9	449
2.2	325
1.2	358
1.4	467
1.8	489
1.2	485
1.1	450
1.4	353
1.8	358
2.3	443
1.7	422
1.3	368
1.5	416

data for the selling prices of homes in a ZIP code and the square footage of those homes. Use the Spearman rank correlation to determine if there is a significant correlation between the home price and the square footage.

Answer 1

Square footage (thousands)	Price of house thousands	Rank(X)	Rank(Y)	Difference, d	d²
2.7	478	2	3	-1	1
2.3	328	5	24.5	-19.5	380.25
2.3	309	5	27	-22	484
1.8	298	16.5	30	-13.5	182.25
1.9	303	13	29	-16	256
2.1	466	10	5	5	25
1.4	328	23	24.5	-1.5	2.25
1.6	385	20	17	3	9
2.1	360	10	20	-10	100
2.9	374	1	18	-17	289
2.2	387	7.5	16	-8.5	72.25
2.6	452	3	7	-4	16
2.1	462	10	6	4	16
1.8	436	16.5	11	5.5	30.25
1.9	424	13	13	0	0
0.95	308	30	28	2	4
1.3	430	25.5	12	13.5	182.25
1.9	449	13	9	4	16
2.2	325	7.5	26	-18.5	342.25
1.2	358	27.5	21.5	6	36
1.4	467	23	4	19	361
1.8	489	16.5	1	15.5	240.25
1.2	485	27.5	2	25.5	650.25
1.1	450	29	8	21	441
1.4	353	23	23	0	0
1.8	358	16.5	21.5	-5	25
2.3	443	5	10	-5	25
1.7	422	19	14	5	25
1.3	368	25.5	19	6.5	42.25
1.5	416	21	15	6	36

Σd² = 4289.5

n = 30

rs = 1 - 6Σd²/(n*(n²-1)) = 1 - 6*4289.5/(30*(30² -1)) = 0.0457

df = n-2 = 28

p-value = 0.8105

As p-value > 0.05, we can conclude that there is no significant correlation between the home price and the square footage.