A Holistic Theoretical Model for Optimal Multiple Linear and Multiple Non Linear Regression Analysis with a Novel Validation Model Scheme for Ensemble Regression Scheme Based Prediction Cases – An Example of Annual Rainfall Prediction
Ramesh Chandra Bagadi *
Department of Civil Engineering, Osmania University, Hyderabad, Telangana, India and Ramesh Bagadi Consulting LLC (R042752), Madison, 53715, Wisconsin, USA.
Suresh Kumar. N
Department Of Civil Engineering, Osmania University, Hyderabad, Telangana, India.
Jagannadharao Basa
uGDX IT, Hyderabad, Telangana, India.
*Author to whom correspondence should be addressed.
Abstract
In this research manuscript note, the authors have advented a comprehensive Holistic Theoretical Model For Optimal Multiple Linear and Multiple Non Linear Regression Analysis. Also, an Exhaustive Error Modeling Scheme is detailed to perfect the advented Model. Furthermore, a Novel Validation Model Scheme is proposed and is illustrated with an example of rainfall forecast. This paper addresses Hyper Space Level Optimization of Linear Regression and Multiple Linear Regression Optimization rather than Optimization in the Number of Independent Parameter Level Dimensions Space in Holistic Independent Parameters Interaction Space at Integral Order that forms a Field, wherein the Hyper Space Dimensions and types are representative of the Interaction of the Independent Parameters themselves. Also, insights into achieving similar results at Fractional orders is also presented. Furthermore, a line of research study that can be performed by scaling such Hyper Spaces Product terms with a Coefficient which represents the Inter Multicollinearity aspect of the Independent Parameters playing role in the Hyper Space effects signifying product terms, is suggested.
Keywords: Multiple linear regression, multiple non-linear regression, linear regression, ensemble linear regression