(a) (b) (c)

Fig. 4.7. Regression model fitness demonstration using R².

ther useful statistic which has been used in ANOVA can also be

measure the fitness of a regression model. It is a ratio of two

and is called the Fisher-statistic or the F-statistic. In regression

this F-statistic is replaced by a different ratio and is called the F-

nston, 1972]. The null hypothesis for using the F-test for assessing

ss of a regression model is ࣢଴: ܨൌ0. The test of the null

is is done by calculating a p value for the significance analysis of

tistic. The F-statistic is defined as below,

ܨൌ

explained variance

unexplained variance

(4.17)

ose N is the number of data points, K is the number of variables

e employed as the independent variables in a regression model.

ained variance is defined as below, where ݕො௡ is the n^th model

stands for the mean of model outputs, i.e., ݕതൌ∑

ݕො௡

ே

௡ୀଵ

ܰ

⁄ ,

corrected sum of squares

rrected degrees of freedom ^ൌ

∑

ሺݕො௡െݕതሻ^ଶ

ே

௡ୀଵ

ܭ

(4.18)

nexplained variance is defined as below,

sum of squares for errors

egrees of freedom for error ^ൌ

∑

ሺݕො

ே

௡ୀଵ

௡^െݕ௡^ሻଶ

ܰെܭ

(4.19)