*2.3. Multiple-Linear Regression*

One of the principal objectives of this study is to quantify the effects of temperature, precipitation, ET, soil moisture at root-zone (NDII), ENSO and DMI on the NDVI as a surrogate for vegetation in the study area. Multiple-linear regression analysis (MLR), which is commonly used to explain the relationship between one continuous dependent variable and two or more independent variables, was employed. The MLR model output of a number *n* observations can be represented as

$$y\_i = \beta\_0 + \beta\_1 \mathbf{x}\_{i2} + \dots + \beta\_p \mathbf{x}\_{ip} + \varepsilon\_i \text{ where } i = 1, 2, 3, \dots, n \tag{4}$$

where *yi* is the dependent variable (NDVI in this case), *xip* represents the independent variables (soil temperature, precipitation, Niño3.4, and DMI in this case), *β*<sup>0</sup> is the intercept, and *β*1, *β*2, ... *β<sup>p</sup>* are the coefficients of the *x* terms. The term ε*<sup>i</sup>* represents the error term, which the model always tries to minimize.
