Abstract: In this paper, the sum of squares in linear regression is
reduced to sum of squares in semi-parametric regression. We
indicated that different sums of squares in the linear regression are
similar to various deviance statements in semi-parametric regression.
In addition to, coefficient of the determination derived in linear
regression model is easily generalized to coefficient of the
determination of the semi-parametric regression model. Then, it is
made an application in order to support the theory of the linear
regression and semi-parametric regression. In this way, study is
supported with a simulated data example.
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.