the correlation matrix is calculated and given as
|
|
Green |
red |
NIR |
|
Green |
1 |
|
|
|
red |
0.9953 |
1 |
|
|
NIR |
0.9750 |
0.9681 |
1 |
correlation between Green and red is highest=r1=0.9953
r1=(n*sum(xy)-sum(x)*sum(y))/sqrt((n*sum(x2)-(sum(x))2)*(n*sum(y2)-(sum(y))2)=0.9953
and same as for r2 and r3
|
s.n. |
green(x) |
red(y) |
NIR(z) |
x2 |
y2 |
z2 |
xy |
xz |
yz |
|
1 |
105 |
128 |
102 |
11025 |
16384 |
10404 |
13440 |
10710 |
10710 |
|
2 |
108 |
129 |
104 |
11664 |
16641 |
10816 |
13932 |
11232 |
11232 |
|
3 |
106 |
128 |
103 |
11236 |
16384 |
10609 |
13568 |
10918 |
10918 |
|
4 |
106 |
129 |
102 |
11236 |
16641 |
10404 |
13674 |
10812 |
10812 |
|
5 |
105 |
130 |
102 |
11025 |
16900 |
10404 |
13650 |
10710 |
10710 |
|
6 |
104 |
128 |
101 |
10816 |
16384 |
10201 |
13312 |
10504 |
10504 |
|
7 |
97 |
115 |
97 |
9409 |
13225 |
9409 |
11155 |
9409 |
9409 |
|
8 |
104 |
124 |
101 |
10816 |
15376 |
10201 |
12896 |
10504 |
10504 |
|
9 |
109 |
133 |
106 |
11881 |
17689 |
11236 |
14497 |
11554 |
11554 |
|
10 |
108 |
134 |
106 |
11664 |
17956 |
11236 |
14472 |
11448 |
11448 |
|
11 |
106 |
128 |
103 |
11236 |
16384 |
10609 |
13568 |
10918 |
10918 |
|
12 |
102 |
125 |
99 |
10404 |
15625 |
9801 |
12750 |
10098 |
10098 |
|
13 |
85 |
95 |
91 |
7225 |
9025 |
8281 |
8075 |
7735 |
7735 |
|
14 |
93 |
109 |
96 |
8649 |
11881 |
9216 |
10137 |
8928 |
8928 |
|
15 |
102 |
125 |
100 |
10404 |
15625 |
10000 |
12750 |
10200 |
10200 |
|
16 |
103 |
124 |
101 |
10609 |
15376 |
10201 |
12772 |
10403 |
10403 |
|
17 |
104 |
126 |
102 |
10816 |
15876 |
10404 |
13104 |
10608 |
10608 |
|
18 |
98 |
118 |
98 |
9604 |
13924 |
9604 |
11564 |
9604 |
9604 |
|
19 |
82 |
89 |
91 |
6724 |
7921 |
8281 |
7298 |
7462 |
7462 |
|
20 |
82 |
94 |
92 |
6724 |
8836 |
8464 |
7708 |
7544 |
7544 |
|
21 |
88 |
102 |
92 |
7744 |
10404 |
8464 |
8976 |
8096 |
8096 |
|
22 |
89 |
101 |
93 |
7921 |
10201 |
8649 |
8989 |
8277 |
8277 |
|
23 |
95 |
112 |
97 |
9025 |
12544 |
9409 |
10640 |
9215 |
9215 |
|
24 |
94 |
108 |
99 |
8836 |
11664 |
9801 |
10152 |
9306 |
9306 |
|
25 |
82 |
89 |
91 |
6724 |
7921 |
8281 |
7298 |
7462 |
7462 |
|
26 |
81 |
89 |
90 |
6561 |
7921 |
8100 |
7209 |
7290 |
7290 |
|
27 |
81 |
93 |
90 |
6561 |
8649 |
8100 |
7533 |
7290 |
7290 |
|
28 |
84 |
95 |
92 |
7056 |
9025 |
8464 |
7980 |
7728 |
7728 |
|
29 |
89 |
104 |
95 |
7921 |
10816 |
9025 |
9256 |
8455 |
8455 |
|
30 |
90 |
104 |
98 |
8100 |
10816 |
9604 |
9360 |
8820 |
8820 |
|
31 |
81 |
90 |
92 |
6561 |
8100 |
8464 |
7290 |
7452 |
7452 |
|
32 |
81 |
89 |
90 |
6561 |
7921 |
8100 |
7209 |
7290 |
7290 |
|
33 |
81 |
89 |
89 |
6561 |
7921 |
7921 |
7209 |
7209 |
7209 |
|
34 |
81 |
90 |
89 |
6561 |
8100 |
7921 |
7290 |
7209 |
7209 |
|
35 |
83 |
92 |
90 |
6889 |
8464 |
8100 |
7636 |
7470 |
7470 |
|
36 |
86 |
96 |
94 |
7396 |
9216 |
8836 |
8256 |
8084 |
8084 |
|
sum |
3375 |
3954 |
3478 |
320145 |
443736 |
337020 |
376605 |
327954 |
327954 |
here we use t-test and statistic would be t
=r/sqrt((1—r2)/(n—2)) with df is n-2=16-2=34
for Green and Red the correlation r1=0.9953,
t=0.9953/sqrt((1-0.9953*0.9953)/(36-2))=59.93 with 34 df
for Green and NIR the correlation r2=0.975,
t=0.975/sqrt((1-0.975*0.975)/(36-2))=25.59 with 34 df
for Green and Red the correlation r3=0.9681
t=0.9681/sqrt((1-0.9681*0.9681)/(36-2))=22.53 with 34 df
typical critical t(0.05,34)=2.03 is less than above calculated
t, so there is significant correlation coefficient i.e. r1,r2 and
r3 are significant
