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hip between the x variable and the y variable is no longer valid in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