A Comparison of the Sum of Squares in Linear and Partial Linear Regression Models
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.
[1] Mayers, Raymond. H., Classical and Modern Regression with
Applications, Duxbury Classical Series, United States, 1990.
[2] Montgomarey, C. Douglas., Peck, A. Elizabeth., Vining, G. Geoffrey.,
Introduction to Linear Regression Analysis, John Wiley&Sons,Inc.,
Toronto, 2001.
[3] Hardle, Wolfang., M├╝ller, Marlene., Sperlich, Stefan., Weratz, Axel.,
Nonparametric and Semiparametric Models, Springer, Berlin, 2004.
[4] Eubank, R. L., Nonparametric Regression and Smoothing Spline, Marcel
Dekker Inc., 1999.
[5] Wahba, G., Spline Model for Observational Data, Siam, Philadelphia
Pa., 1990.
[6] Green, P.J. and Silverman, B.W., Nonparametric Regression and
Generalized Linear Models, Chapman & Hall, 1994.
[7] Schimek, G. Michael, Estimation and Inference in Partially Linear
Models with Smoothing Splines, Journal of Statistical Planning and
Inference, 91, 525-540, 2000.
[8] Hastie, T.J. and Tibshirani, R.J., Generalized Additive Models,
Chapman & Hall /CRC, 1999.
[9] Wood, N. Simon., Generalized Additive Models An Introduction With
R, Chapman & Hall/CRC, New York, 2006.
[10] Hastie, T., The gam Package, Generalized Additive Models, R topic
documented,
http://cran.r.project.org/packages/gam.pdf, February 16, 2008.
[1] Mayers, Raymond. H., Classical and Modern Regression with
Applications, Duxbury Classical Series, United States, 1990.
[2] Montgomarey, C. Douglas., Peck, A. Elizabeth., Vining, G. Geoffrey.,
Introduction to Linear Regression Analysis, John Wiley&Sons,Inc.,
Toronto, 2001.
[3] Hardle, Wolfang., M├╝ller, Marlene., Sperlich, Stefan., Weratz, Axel.,
Nonparametric and Semiparametric Models, Springer, Berlin, 2004.
[4] Eubank, R. L., Nonparametric Regression and Smoothing Spline, Marcel
Dekker Inc., 1999.
[5] Wahba, G., Spline Model for Observational Data, Siam, Philadelphia
Pa., 1990.
[6] Green, P.J. and Silverman, B.W., Nonparametric Regression and
Generalized Linear Models, Chapman & Hall, 1994.
[7] Schimek, G. Michael, Estimation and Inference in Partially Linear
Models with Smoothing Splines, Journal of Statistical Planning and
Inference, 91, 525-540, 2000.
[8] Hastie, T.J. and Tibshirani, R.J., Generalized Additive Models,
Chapman & Hall /CRC, 1999.
[9] Wood, N. Simon., Generalized Additive Models An Introduction With
R, Chapman & Hall/CRC, New York, 2006.
[10] Hastie, T., The gam Package, Generalized Additive Models, R topic
documented,
http://cran.r.project.org/packages/gam.pdf, February 16, 2008.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:58873", author = "Dursun Aydın", title = "A Comparison of the Sum of Squares in Linear and Partial Linear Regression Models", 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.", keywords = "Partial Linear Regression Model, Linear RegressionModel, Residuals, Deviance, Smoothing Spline.", volume = "2", number = "6", pages = "342-7", }