2.4. Multi-linear regression analysis
The MLRA (multi-linear regression analysis), a statistical technique
used to model the relationships between a dependent variable and one or
more independent variables was used to characterize, trends, annual and
semi-annual amplitudes in rainfall. It uses a least square approach and
has been widely applied in hydrology and climate science to explain the
possible relationships between key variables (see, e.g., Ndehedehe et
al., 2016a; Rieser et al., 2010). The focus here is to separate the
harmonic components (mean annual and semi-annual amplitudes) of rainfall
over different 30-year climatological periods (1901- 2014) and
then compare whether they are statistically different or have different
means using analysis of variance (ANOVA). ANOVA is a prominent
statistical method that is employed to assesses if the means of two or
more groups (in our case, trends, mean annual and semi-annual rainfall
patterns from each climatological period) are significantly different
from each other. In the MLRA technique, the trends and harmonic
components (mean annual and semi-annual amplitudes) for each
climatological period (1901- 1930; 1931- 1960;
1961- 1990; 1991- 2010) were compartmentalised from the
precipitation time series (P ) through parameterizations as (e.g.,
Ndehedehe and Ferreira, 2020; Rieser et al., 2010),
P (l, k, t ) =β0 +
β1t + β2sin (2πt ) +
β3cos (2πt ) +
β4sin (4πt ) +
β5cos (4πt ) + ε(t ); ( 2)
where (l; k ) are the grid locations, t is the time
component, β0 is the constant offset, β1is the linear trend, β2 and β3 account
for the annual signal, β4 and β5represent the semi-annual signal, while ε(t ) is the random error
term. The amplitudes of rainfall (i.e., mean annual and semi-annual)
over the region are then estimated as,
\(Annual\ =\left[\left(\ \beta 2\right)^{2}+\ \ \left(\ \beta 3\right)^{2}\ \right]^{\frac{1}{2}}\)and \(\text{\ Semi\ }Annual=\)\(\left[\left(\ \beta 4\right)^{2}+\ \ \left(\ \beta 5\right)^{2}\ \right]^{\frac{1}{2}}\)(3)