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.