X Y
Survey No. Advisor x-xbar (x-xbar)2 Quality Exp. y-ybar (y-ybar)2 (x-xbar)(y-ybar)
1 2.00 -0.7 0.49 4.0 0.37 0.14 -0.26
2 3.00 0.3 0.09 4.0 0.37 0.14 0.11 Correlation Coefficient or Pearson's r
3 4.00 1.3 1.69 4.0 0.37 0.14 0.48
4 4.00 1.3 1.69 4.0 0.37 0.14 0.48
5 4.00 1.3 1.69 4.0 0.37 0.14 0.48
6 2.00 -0.7 0.49 4.0 0.37 0.14 -0.26
7 4.00 1.3 1.69 4.0 0.37 0.14 0.48
8 3.00 0.3 0.09 3.0 -0.63 0.40 -0.19
9 2.00 -0.7 0.49 3.0 -0.63 0.40 0.44
10 2.00 -0.7 0.49 3.0 -0.63 0.40 0.44
11 3.00 0.3 0.09 4.0 0.37 0.14 0.11
12 4.00 1.3 1.69 4.0 0.37 0.14 0.48
13 2.00 -0.7 0.49 2.0 -1.63 2.66 1.14
14 3.00 0.3 0.09 4.0 0.37 0.14 0.11
15 3.00 0.3 0.09 2.0 -1.63 2.66 -0.49
16 3.00 0.3 0.09 3.0 -0.63 0.40 -0.19
17 4.00 1.3 1.69 4.0 0.37 0.14 0.48
18 0.00 -2.7 7.29 4.0 0.37 0.14 -1.00
19 1.00 -1.7 2.89 3.0 -0.63 0.40 1.07
20 2.00 -0.7 0.49 4.0 0.37 0.14 -0.26
21 4.00 1.3 1.69 4.0 0.37 0.14 0.48
22 3.00 0.3 0.09 4.0 0.37 0.14 0.11
23 4.00 1.3 1.69 4.0 0.37 0.14 0.48
24 3.00 0.3 0.09 4.0 0.37 0.14 0.11
25 1.00 -1.7 2.89 2.0 -1.63 2.66 2.77
26 4.00 1.3 1.69 4.0 0.37 0.14 0.48
27 4.00 1.3 1.69 4.0 0.37 0.14 0.48 Covariance of x & y
28 1.00 -1.7 2.89 3.0 -0.63 0.40 1.07
29 3.00 0.3 0.09 4.0 0.37 0.14 0.11
30 2.00 -0.7 0.49 4.0 0.37 0.14 -0.26
31 4.00 1.3 1.69 4.0 0.37 0.14 0.48
32 4.00 1.3 1.69 4.0 0.37 0.14 0.48
33 3.00 0.3 0.09 3.0 -0.63 0.40 -0.19
34 2.00 -0.7 0.49 4.0 0.37 0.14 -0.26
35 1.00 -1.7 2.89 3.0 -0.63 0.40 1.07
36 3.00 0.3 0.09 4.0 0.37 0.14 0.11
37 2.00 -0.7 0.49 3.0 -0.63 0.40 0.44
38 3.00 0.3 0.09 4.0 0.37 0.14 0.11
39 1.00 -1.7 2.89 -3.63 13.18 6.17
40 3.00 0.3 0.09 3.0 -0.63 0.40 -0.19
41 1.00 -1.7 2.89 3.0 -0.63 0.40 1.07
42 1.00 -1.7 2.89 3.0 -0.63 0.40 1.07
43 2.00 -0.7 0.49 3.0 -0.63 0.40 0.44
44 3.00 0.3 0.09 4.0 0.37 0.14 0.11
45 3.00 0.3 0.09 4.0 0.37 0.14 0.11
46 1.00 -1.7 2.89 4.0 0.37 0.14 -0.63
47 4.00 1.3 1.69 4.0 0.37 0.14 0.48
48 2.00 -0.7 0.49 3.0 -0.63 0.40 0.44
49 1.00 -1.7 2.89 4.0 0.37 0.14 -0.63
50 3.00 0.3 0.09 4.0 0.37 0.14 0.11
51 2.00 -0.7 0.49 4.0 0.37 0.14 -0.26
52 4.00 1.3 1.69 3.0 -0.63 0.40 -0.82
53 3.00 0.3 0.09 4.0 0.37 0.14 0.11
54 4.00 1.3 1.69 4.0 0.37 0.14 0.48
55 2.00 -0.7 0.49 -3.63 13.18 2.54
56 3.00 0.3 0.09 4.0 0.37 0.14 0.11
57 4.00 1.3 1.69 4.0 0.37 0.14 0.48
58 4.00 1.3 1.69 4.0 0.37 0.14 0.48
59 2.00 -0.7 0.49 4.0 0.37 0.14 -0.26
60 3.00 0.3 0.09 4.0 0.37 0.14 0.11
61 4.00 1.3 1.69 4.0 0.37 0.14 0.48
62 1.00 -1.7 2.89 2.0 -1.63 2.66 2.77
63 2.00 -0.7 0.49 3.0 -0.63 0.40 0.44
64 1.00 -1.7 2.89 3.0 -0.63 0.40 1.07
65 2.00 -0.7 0.49 4.0 0.37 0.14 -0.26
66 3.00 0.3 0.09 3.0 -0.63 0.40 -0.19
67 3.00 0.3 0.09 4.0 0.37 0.14 0.11
68 4.00 1.3 1.69 4.0 0.37 0.14 0.48
69 2.00 -0.7 0.49 3.0 -0.63 0.40 0.44
70 2.00 -0.7 0.49 4.0 0.37 0.14 -0.26
71 3.00 0.3 0.09 4.0 0.37 0.14 0.11
72 4.00 1.3 1.69 4.0 0.37 0.14 0.48
73 2.00 -0.7 0.49 4.0 0.37 0.14 -0.26
74 2.00 -0.7 0.49 4.0 0.37 0.14 -0.26
75 2.00 -0.7 0.49 4.0 0.37 0.14 -0.26
76 2.00 -0.7 0.49 3.0 -0.63 0.40 0.44
77 3.00 0.3 0.09 4.0 0.37 0.14 0.11
78 4.00 1.3 1.69 4.0 0.37 0.14 0.48
79 4.00 1.3 1.69 3.0 -0.63 0.40 -0.82
80 3.00 0.3 0.09 4.0 0.37 0.14 0.11
81 4.00 1.3 1.69 4.0 0.37 0.14 0.48
xbar 2.70 ybar 3.63 Sum((x-xbar)(y-ybar)) 29.01
Sum(x-xbar)2
 90.89
Sum(y-ybar)2
 52.71
r =
 Sum((x-xbar)(y-ybar))
=
29.01
Sq. Root((Sum(x-xbar)2)*(Sum(y-ybar)2))
Sq. Root(90.89*52.71)
29.01 = 29.01 = 0.42
sq.root 4790.71 69.21
Therefore, the rating for overall quality of the program is positively correlated
with the rating of the helpfulness of the advisor (r=0.42).
To see if the correlation is significantly different from zero, you conduct a t-test using the following formula:
t=r*sqroot(n-2)/sqroot(1-r^2)
 For p<.01, t=2.660 at 60 df df=n-2=79
  t= 4.103441846   p<.01
   
             
To estimate the amount of variance accounted for by this correlation, simply square the correlation.
rsquare =
 0.18
This correlation accounts for roughly eighteen percent of the variance (rsquare = 0.18).