2.5 Linear regression analysis
A time series y1, y2 …, yi, …, yn can be calculated by the Eq. (7) used by Tang et al. (2011):
\(\hat{y_{n}}=a_{0}+a_{1}t+\ldots+a_{m}t^{n}\ \ \ \ (m<n)\)………………………………… ………(7)
Where yi = the response variable (i.e. ET0, precipitation), t = the year. Generally, the linear trend of a time series can be estimated by the least square method and can be expressed by a linear regression Eq. (8) as:
\(\hat{y_{n}}(t)=a_{0}+a_{1}t\)…………………………………………………………… …….(8)
where the slope a1 is the estimated trend, and\(\text{\ a}1\times 10\) is called climate tendency rate, which presents its change rate. Negative value of a1represents a negative trend while positive value of a1represents a positive trend.