Figure 3. Time series plot of the variables
Using MATLAB curve fitting toolbox, the linear regression of population is a good fit with an adjusted R2 of 97.93% and an RMSE of 3.13 x103 (see supplemental I for the coefficients). However, quadratic regression is a better fit with an adjusted R2 of 99.95% and an RMSE of 5.069 x104. It also shows that the population is concave up (Figure 4.a). In other words the rate of population increase is also increasing over the time. We have de-trended the population data to learn more about the population variations and possible connections to crop yields. As shown in figure 4b the Gaussian model has identified two significant population variations: a population decline of 50,000 below the trend value in 1998 (t = 26) and a population spike of more than 100,000 above the trend value in 2005. During the years 2005 -2011, the de-trended population data declines more than 200,000, which indicates a significant decline in the population growth.
We followed the same above approach to de-trend precipitation data. Changing from linear to quadratic or cubic regression does not improve the model. The adjusted R2 for linear, quadratic and cubic models are, 46.76%, 45.19%, and 49.25%, respectively; see supplemental II for the coefficients. Therefore, we choose the linear regression (Figure 4.c). After de-trending the precipitation data, the fitted Gaussian model identified a significant ditch with the minimum value in the year 1983. As shown in Figure 4d, there is a ditch from 600 to -600 and going back to 160 during the years 1980 to 1990.