Question

How much variance in grades is explained by artistic sensitivity? Show how you derived your answer

students	AS	G
1	8	81
2	9	97
3	8	72
4	7	79
5	6	70
6	4	60
7	6	81
8	7	87
9	6	77
10	0	85
11	6	64
12	7	91
13	8	75
14	7	73
15	7	76
16	8	83
17	8	83
18	2	55
19	8	92
20	9	92
21	8	90
22	7	62
23	9	85
24	7	57
25	5	82
26	9	91
27	8	69
28	5	66
29	9	88
30	8	74

Answer 1

y: Grades

x: artistic sensitivity.

First, we have to find the correlation coefficient between x and y.

Formula is

n = 30

students	x	y	xy	x^2	y^2
1	8	81	648	64	6561
2	9	97	873	81	9409
3	8	72	576	64	5184
4	7	79	553	49	6241
5	6	70	420	36	4900
6	4	60	240	16	3600
7	6	81	486	36	6561
8	7	87	609	49	7569
9	6	77	462	36	5929
10	0	85	0	0	7225
11	6	64	384	36	4096
12	7	91	637	49	8281
13	8	75	600	64	5625
14	7	73	511	49	5329
15	7	76	532	49	5776
16	8	83	664	64	6889
17	8	83	664	64	6889
18	2	55	110	4	3025
19	8	92	736	64	8464
20	9	92	828	81	8464
21	8	90	720	64	8100
22	7	62	434	49	3844
23	9	85	765	81	7225
24	7	57	399	49	3249
25	5	82	410	25	6724
26	9	91	819	81	8281
27	8	69	552	64	4761
28	5	66	330	25	4356
29	9	88	792	81	7744
30	8	74	592	64	5476
Total	206	2337	16346	1538	185777

Now we have to find R^2

R^2 = r^2 = 0.4403^2 = 0.1939

19.39% variance in grades is explained by artistic sensitivity.