*4.2. Trends of Correlation Coe*ffi*cients for Root Mean Square and Logarithm Reciprocal*

Correlation analysis is a key step in spectral data preprocessing. When the correlation coefficient between available potassium and spectral signal passes the significance test, the corresponding band is likely to become the sensitive band, and the band reflectance can be used as the independent variable in the model to establish a reliable predictive model of available potassium content. In this paper, the significance test was carried out at 0.05 level, and the calculus was programmed in Matlab software (MathWorks, Natick, MA, USA) to calculate the correlation between the spectral reflectance and the available potassium content after root mean square and logarithmic inverse transformation, and the differential results between 0-order and 2-order were calculated (at intervals of 0.2). The simulation results are shown in Figures 4 and 5. When differential order gradually increases from zero-order to first-order, the curve of correlation coefficient shows a certain gradual change trend. When the order is increased from 1-order to 2-order, correlation coefficient curve fluctuates greatly, and the gradual change trend is not obvious.

**Figure 4.** Trends of correlation coefficient for root mean square: (**a**) 0-order to 0.4-order; (**b**) 0.6-order to 1-order; (**c**) 1.2-order to 1.4-order; and (**d**) 1.6-order to 2-order.

**Figure 5.** Trends of correlation coefficient for logarithm reciprocal: (**a**) 0-order to 0.4-order; (**b**) 0.6-order to 1-order; (**c**) 1.2-order to 1.4-order; and (**d**) 1.6-order to 2-order.
