d by one unit at three positions, the y variable does not change

nally in a constant. This means that the proportional and linear

hip between the x variable and the y variable is no longer valid in

ear regression model. In other words, the relationship between

in a nonlinear model will not be held as a constant.

ssion analysis has been widely used in pattern discovery for

cades. The earliest record of regression analysis in PubMed was

ng research [Orcutt and Cochrane, 1949]. In spite of this,

n analysis still plays an important role for biological/medical

nalysis [Kumaran, et al., 2020; Kwon, et al., 2020].

ordinary linear regression analysis algorithm

lest regression analysis approach is the ordinary linear regression

m (OLR). Without using any constraint, the parameters of an OLR

e estimated using the simplest approach, i.e., the least squared

proach. The approach estimates model parameters through

ng the total regression error.

e least squared error approach

ing an OLR model requires the model parameters (α and β) to be

d using the least squared error approach (LSE). In a regression

n error is defined as the distance between an observed outcome y

edicted outcome ݕො from a regression model. ݕො is also called the

mean variable or the model output variable or the regression

n variable. In order to use LSE to estimate model parameters, the

of regression errors should be introduced at first.

ݕො is obtained or predicted from a regression analysis model after

el parameters (ߙ and ߚ) have been accurately estimated. The

between ݕො and y is named as the regression error, which is defined

where the regressed mean function is defined as ݕොൌߙ൅ ߚݔ ,