The stepwise linear regression (SLR) model is often used to assess the linear relationship between multiple independent variables and it can be used for variable screening and avoided collinearity for soil nutrient prediction [16]. Stepwise regression can also be used for variable screening. SLR can remove the weakly significant variables while retaining those with high contribution rate. In this study, the SLR model was used to identify the optimal combination of input PCs with targets. The linear fitting relationships between hyperspectral auxiliary variables and soil nutrients were also extracted. The SLR model was performed in MATLAB 2013b software. The formula of SLR model (Equation (1)) is defined as follows [32]:
y = b + a 1 x 1 + · · · + a k x k ,(1)
where y is the estimation value of SLR for soil nutrients, b is a regression constant, a 1 , . . . , a k are regression coefficients and x 1 , . . . , x k are the input PCs converted from hyperspectral variables. The support vector machine (SVM) model is a supervised learning method that was used to solve the regression problem in this study. The SVM method can identify the separating optimal hyperplane in multi-dimensional spatial **data** and seeks to minimize the error of all training samples. The SVM model overcomes the limitation of neural networks, which tend to rely on local optimal solutions [33]. Therefore, the SVM model is well suited to soil nutrient prediction with multi-dimensional variables.