Abstract: The focus in this work is to assess which method
allows a better forecasting of malaria cases in Bujumbura ( Burundi)
when taking into account association between climatic factors and
the disease. For the period 1996-2007, real monthly data on both
malaria epidemiology and climate in Bujumbura are described and
analyzed. We propose a hierarchical approach to achieve our
objective. We first fit a Generalized Additive Model to malaria cases
to obtain an accurate predictor, which is then used to predict future
observations. Various well-known forecasting methods are compared
leading to different results. Based on in-sample mean average
percentage error (MAPE), the multiplicative exponential smoothing
state space model with multiplicative error and seasonality performed
better.
Abstract: In this paper, estimation of the linear regression
model is made by ordinary least squares method and the
partially linear regression model is estimated by penalized
least squares method using smoothing spline. Then, it is
investigated that differences and similarity in the sum of
squares related for linear regression and partial linear
regression models (semi-parametric regression models). It is
denoted that the sum of squares in linear regression is reduced
to sum of squares in partial linear regression models.
Furthermore, we indicated that various sums of squares in the
linear regression are similar to different deviance statements in
partial linear regression. In addition to, coefficient of the
determination derived in linear regression model is easily
generalized to coefficient of the determination of the partial
linear regression model. For this aim, it is made two different
applications. A simulated and a real data set are considered to
prove the claim mentioned here. In this way, this study is
supported with a simulation and a real data example.