343 
whole 
onents 
ponents 
Components 
then the four 
-i; j = 1, 4 ) 
les less than 
= 10, 20, 30, 
and data can 
it is possible 
data on an 
action cosines 
requirement. 
•d reflectance 
>s 
n determined 
:hnique (Mitai 
with a corre 
cted, whose 
i observations 
pies for each 
del for large 
ie number of 
of India has 
i/lunsell colour 
roma 1 to 6. 
been observed 
ons described 
so been deter- 
model based 
been evolved 
. The values 
>del, six more 
falling within 
ollected from 
ill these sam- 
e values were 
in sizes were 
idicted values 
mined in the 
between the 
Table 2. Regression analysis of diamter on transformed data 
Number of samples = 5 
num variance 
ixed axes in 
Regression Constants for diameter on 
ppc 3 
Regression constants for diamter on PPC 
x and SPC 
ied regression 
ctor variables 
ig them, will 
Hence, the 
SI.No 
Dia 
< d x> 
C 
X 
M 
X 
<fy 
GjT.x 
r 
A 
X 
B 
X 
C 
X 
<Ty.xl.x2 
r 
1 
d 10 
0.224 
0.167 
0.158 
0.133 
0.683 
-6.11 
5.30 
-1.37 
0.137 
0.79 
btained, have 
2 
d 20 
0.293 
0.369 
0.293 
0.196 
0.815 
-13.95 
12.17 
-3.36 
0.147 
0.93 
ultiple linear 
n found that 
3 
d 30 
0.391 
0.568 
0.474 
0.345 
0.776 
-23.28 
20.14 
-5.55 
0.191 
0.96 
fourth PPC 
4 
d 40 
0.469 
0.785 
0.648 
0.463 
0.785 
-32.64 
28.30 
-7.92 
0.140 
0.99 
pendent vari- 
of 0.94 for 
5 
d 50 
0.786 
0.919 
0.867 
0.728 
0.686 
-44.60 
38.28 
-10.46 
0.094 
0.99 
-linear model 
6 
d 60 
1.299 
1.065 
1.121 
1.019 
0.615 
-57.51 
49.40 
-13.46 
0.132 
0.99 
7 
d 7Q 
2.291 
1.049 
1.102 
1.000 
0.616 
-54.90 
48.29 
-13.35 
0.234 
0.98 
8 
d 80 
4.110 
0.468 
0.498 
0.456 
0.609 
-21.24 
21.42 
-5.94 
0.167 
0.97 
9 
d 90 
6.317 
-0.223 
0.378 
0.403 
0.382 
-2.44 
6.06 
-0.99 
0.312 
0.81 
- Slope coefficient 
- y intercept 
regression coefficient 
standard deviation of diameters 
- standard error of estimate 
A x , B^, C x - partial regression coefficients 
<Ty xl x2 ~ stan< ^ arc l error °f estimate 
r J - multiple correlation coefficient 
Table 3. Grain size prediction model by optimization 
Number of samples = 5 
SI. No. 
Description of model 
Correlation coefficient of diameter with 
Transformed 
data 
Original data in 
Band-7| 
Band-6 | 
Band-5 1 
Band-4 
1 
«10 =<0.22B 7 
- 0.55B 6 + 0.62B 5 - 0.50B^) 1.08 + 1.53 
1.0 
-0.21 
-0.20 
-0.22 
-0.40 
2 
d 20 =<0.24B 7 - 
0.52B 6 + 0.60B 3 - 0.55B^) 1.65 + 2.42 
1.0 
0.13 
0.13 
0.07 
-0.09 
3 
d 3Q =(0.24B ? 
- 0.52B 6 + 0.61B 5 - 0.54B^) 2.75 + 3.61 
1.0 
0.23 
0.24 
-0.18 
0.01 
4. 
d, 0 =<0.25B 7 
- 0.51B 6 + 0.59B 5 - 0.57B 4 ) 3.31 + 4.65 
1.0 
0.34 
0.30 
0.21 
0.10 
5 
d 5Q =<0.25B 7 
- 0.54B 6 + 0.60B 5 - 0.53B^) 4.97 + 6.28 
1.0 
0.40 
0.29 
0.19 
0.17 
6 
d 60 = (0 - 2 ' ,B 7 
- 0.54B 6 + 0.61B 5 - 0.51B 4 ) 6.29 + 7.49 
1.0 
0.51 
0.39 
0.29 
0.30 
7 
d 7Q =<0.25B 7 
- 0.53B 6 + 0.60B 3 - 0.53B^) 5.44 + 7.81 
1.0 
0.58 
0.45 
0.34 
0.36 
8 
d 80 =<0.26B 7 
- 0.53B 6 + 0.59B 5 - 0.54B^) 2.27 + 6.70 
1.0 
0.57 
0.38 
0.24 
0.34 
9 
d 90 =<0.21B 7 
- 0.64B 6 + 0.67B 5 - 0.28B 4 ) 2.37 + 6.63 
1.0 
0.46 
0.17 
0.10 
0.48 
Table 4. Regression analysis of diameter on original and transformed data 
Number of samples = 14 
SI.No 
Dia 
r- values with original data in 
Regression 
constants for the model 
Band-7 
Band-6 
Band-5 
Band-4 
C 
X 
M 
X 
<r y 
ffT.x 
r 
1 
d 10 
-0.94 
-0.88 
-0.80 
-0.61 
1.21 
0.05 
0.22 
0.07 
0.95 
2 
d 20 
-0.92 
-0.85 
-0.69 
-0.61 
2.25 
0.12 
0.45 
0.09 
0.98 
3 
d 30 
-0.92 
-0.85 
-0.70 
-0.52 
3.35 
0.18 
0.67 
0.15 
0.98 
4 
-0.90 
-0.82 
-0.67 
-0.53 
5.02 
0.32 
1.07 
0.32 
0.96 
5 
d 50 
-0.87 
-0.79 
-0.63 
-0.53 
6.74 
0.46 
1.49 
0.54 
0.94 
6 
d 60 
-0.83 
-0.74 
-0.58 
-0.50 
8.37 
0.64 
1.87 
0.77 
0.92 
7 
d 70 
-0.74 
-0.67 
-0.51 
-0.51 
9.62 
0.81 
2.17 
1.17 
0.85 
8 
d 80 
-0.67 
-0.62 
-0.48 
-0.51 
11.24 
0.93 
2.45 
1.44 
0.82 
9 
d 90 
-0.51 
-0.49 
-0.40 
-0.64 
12.00 
1.03 
2.15 
1.36 
0.80