Question

1. Determine statistically which two bands are the most correlated? Explain how did you get your answer and include intermediate calculations.

105 97 85 82 82 81 108 104 93 82 81 81 106 109 102 88 81 81 106 108 103 89 84 81 105 106 104 95 89 83 104 102 98 94 90 86 Green

128 115 95 89 89 90 129 124 109 94 89 89 128 133 125 102 93 89 129 134 124 101 95 90 130 128 126 112 104 92 128 125 118 108 104 96 Red

102 97 91 91 91 92 104 101 96 92 90 90 103 106 100 92 90 89 102 106 101 93 92 89 102 103 102 97 95 90 101 99 98 99 98 94 NIR

Answer 1

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