The ionosphere, also known as the ionized part of the upper atmosphere, is believed to vary as a function of different parameters such as solar and geomagnetic activities. One of the peculiar parameters that describe the variability of the ionosphere is its total electron content (TEC). This work focuses on modeling the variability of the daily TEC as a function of F10.7 flux and MgII using modeling over Assosa, Ethiopia. The analysis was done for 2012-2015 TEC data sets. From the modeling, we could infer both the linear and non-linear trends of the TEC as a function of F10.7 and MgII. We have also predicted the daily VTEC for each year under consideration. The deviation between the modeled TEC and the observation has a clear daily and seasonal variation. Specifically, we could observe high deviation during equinox than solstice seasons. Both the short-term and long-term analysis of the modeling depicted that the linear variation of TEC as a function of F10.7 and MgII is more dominant than the non-linear variation. We came to conclude that on average, the proposed linear time series model could explain 80% of the variation of vTEC.