(a) (b)

Fig. 4.6. The fitness scenarios of two regression models.

tudy of the regression model fitness aims to measure how good a

n model is in relationship with the regression error. The R-

(also denoted as R²), which is also called a coefficient

ation, is one of the measurements. It measures how good a

n model fits to data regardless how a model is constructed [Steel

e, 1962]. The definition of R² is shown below, which is metric-

ce can be used for comparing different models constructed on

data,

R^ଶൌ1 െ

∑

ߝ௡^ଶ

ே

௡ୀଵ

ሺܰെ1ሻߪ^ଶ

(4.15)

xplanation of the R² is shown below,

R^ଶൌ1 െ^{variance explained by a model}

totla variance

(4.16)

= 1, a regression model fits the data completely because the

explained by a regression model is zero. In other words, there is

ce between the observations and the regressed means in a model.

a regression model completely fails to fit the data because the

ance between the observations and the regressed means is the

the variance of the dependent variable. Figure 4.7 shows three

where the fitness measurement was from the largest (0.9531) to

est (0.0049). Through comparing these three models, it can be

the model shown in Figure 4.7(a) was the best with the highest