y

,

y

n models have the difficulty of explaining why and how a

n is made.

he principle of a regression analysis — regressing to mean. The dots are the

ata (the collected data points). The triangles are the regressed means. The

tween the observed data and their regressed means are the regression errors.

ne represents the regressed regression function, which is to be estimated through

ation process based on the regressed means, i.e., the five triangles.

ression model can be either univariate or multivariate depending

mber of the repressors or the independent variables employed in

on model. In a univariate regression model, only the relationship

two variables is examined. One variable is an independent

(x) and the other is a dependent variable (y). The relationship

at y can be explained or interpreted by x in a linear way. Its formal

is shown below, where ߙ is the intercept, ߚ is the regression

nt and ߝ is the regression error

ݕ ൌߙ൅ߚݔ൅ߝ



above equation, ߝ interprets how good the regression model is

erprets how y depends on x. For instance, when one unit change

ened in x, ߚ units change will happen in y accordingly. Figure 4.3

uch a model. The relationship between two variables in this

e regression model is defined as below,