Question

The following data on x = score on a measure of test anxiety and y = exam score for a sample of n = 9 students are consistent with summary quantities given in a paper. Higher values for x indicate higher levels of anxiety. Compute the value of the correlation coefficient. (Give the answer to four decimal places.)
r = ________

x	23	13	15	0	17	21	19	14	20
y	44	59	49	76	49	51	46	52	51

Answer 1

Solution:

The correlation coefficient formula is given as below:

Correlation coefficient = r = [n∑xy - ∑x∑y]/sqrt[(n∑x^2 – (∑x)^2)*(n∑y^2 – (∑y)^2)]

The calculation table is given as below:

No.	x	y	x^2	y^2	xy
1	23	44	529	1936	1012
2	13	59	169	3481	767
3	15	49	225	2401	735
4	0	76	0	5776	0
5	17	49	289	2401	833
6	21	51	441	2601	1071
7	19	46	361	2116	874
8	14	52	196	2704	728
9	20	51	400	2601	1020
Total	142	477	2610	26017	7040

From above table, we have

n = 9

∑x = 142

∑y = 477

∑x^2 = 2610

∑y^2 = 26017

∑xy = 7040

r = [n∑xy - ∑x∑y]/sqrt[(n∑x^2 – (∑x)^2)*(n∑y^2 – (∑y)^2)]

r = [9*7040 - 142*477]/sqrt[(9*2610– (142)^2)*(9*26017– (477)^2)]

r = [-4374]/sqrt[(23490 – 20164)*( 234153 – 227529)]

r = -4374 /sqrt(22031424)

r = -4374 /4693.764

r = -0.93187

r = -0.9319

There is a very strong negative linear relationship exists between the given two variables.