The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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I U t -Y) 2 [!.(¥'-YXY,-Y t )] 2 
R 2 =~ — = — 1 = — = 
i(T,-Y) 2 itf-ry-iItf-Y) 2 
i=1 M /=1 
(5) 
However, the value of validation coefficient^ is increased 
along with the increasing amount of independent variable n (or 
sample capacity). Therefore, to reflect as accurately as possible 
the fitting degree of model and eliminate the effects of 
independent variable amount and sample size on validation 
coefficient, the adjusted validation coefficient (Adjusted R 
Square) is introduced. Its formula is: 
UY-Yf !{n-k-\) 
AdjustedR 2 =1—— — (6) 
i(Y-Y) 2 !{n-\) 
/=1 
In the formula, ^ is the amount of independent variables 
(number of selected wavebands), ^ is the amount of observe 
objectives (number of samples). When the amount of 
independent variables is more than 1, the value of adjusted R2 is 
less than validation coefficient R2. As shown in the formulas, 
the larger n is, the greater difference between R2 and adjusted 
R2. 
The accuracy of predictive equation is evaluated by the total 
root-mean-square error ( 1XiVlk ~ >L ^ ) (formula 7). 
RMSE= J—-—- Z(f -Îj) 2 
V n—k—\i=1 
In the formula, 1 and 1 represent measured value and 
predictive value, n is the amount of soil samples, ^ is the 
amount of selected wavebands. 
After establishment of the edpBnon, variance analysis was also 
used to test the regression equation. The hypothesis of test was 
that the global regression coefficients are 0 or not 0, and it was 
the significance test for the whole regression equation. 
3 ANALYSIS AND RESULTS 
3.1 Correlation analytic results 
The SOM contents of 174 soil samples were measured by 
volumetry assay, the minimal value is 0.12% and the maximal 
value is 4.86%, and the mean value is 1.18%. The mean square 
deviation was 1.12. The correlation coefficient between 
measured SOM content and smoothed spectral reflectance at the 
range of 350nm-2500nm was calculated according to formula 4. 
The results indicated that, the transforms, except the logarithmic 
reciprocal of reflectance, all increased correlation of soil 
organic matter content to some extent. Among them, the most 
significant was the first order differential transforms for 
reflectance logarithm. The maximal correlation coefficient 
between original reflectance before transforming and SOM 
content was 0.72 (at 2137 nm wavelength), while correlation 
coefficient between first order differential transforms of 
reflectance logarithm and SOM content at 2187 nm was 0.89, 
the maximum of all correlation coefficients (Figure 3). This also 
indicated that some subtle information obscured in original 
spectral data was amplified and made clear after differential 
transformation. 
500 1000 1500 2000 2500 
Wavelertgth(nm) 
Figure. 3 Correlation Coefficients between (lg/?)' and SOM 
Content 
The analytic results also manifested that, SOM content was 
negative correlated with spectral reflectance but positive 
correlated with the reciprocal of reflectance, and the change 
trend of absolute values of both correlation coefficients was 
basically consistent. The changes of correlation coefficients 
between differential transforms (both first and second order) 
and SOM displayed no rule, different from the mild changes in 
correlation coefficients of logarithmic and reciprocal transforms. 
Its value oscillates between 1 and -1. 
3.2 Stepwise regression results 
Stepwise regression analysis methods commonly used to 
identify the wavebands sensitive to a certain chemical 
constituent, and to demonstrate these wavebands has a good 
correlation with the concentration of a certain chemical 
constituent. Accordingly, we can use these determined locations 
of the wavelength (band values) to estimate the concentration of 
a certain chemical composition. However, there are two aspects 
of deficiency: firstly, there exists overfitting phenomenon in 
establishment of regression model. This phenomenon mainly 
appears while the sample size is less than the amount of 
wavebands. Then spectral reflectance values may not correlated 
with certain chemical composition while its noise pattern may 
be related to certain chemical composition. This kind of risk is 
increasing along with increase of the number of wavebands. 
Secondly, the deficiency is highly correlation among wavebands. 
An important hypothesis of stepwise regression method is that 
some input variables in multiple regression analysis have no 
significant impact on output. If this assumption is valid, it is 
easy to simplify the model, retaining only those items with 
statistical significance. But, in fact, multiple interactions exist