nce test for each regression coefficient. It calculates the following

Weisberg, 2005], where ߚ^መ௜ is the estimated regression coefficient

independent variable,

ݐൌ

ߚ^መ௜

seሺߚ^መ௜ሻ

(4.20)

eሺߚ^መ௜ሻ is calculated using the following formula and ߤ௫೔ൌ

ܰ,

seሺߚ^መ௜ሻൌඨ

∑

ሺݕො௡െݕ௡ሻ^ଶ

ே

௡ୀଵ

ܰെ2

⁄

∑

൫ݔ௜െߤ௫೔൯

ଶ

ே

௡ୀଵ

(4.21)

regression models are shown in Figure 4.9. Both had a large

noise (variance). The regression coefficient was 0.3606 in Figure

d was 0.0102 in Figure 4.9(b). Their p values were 0.0192 and

n Figures 4.9(a) and (b), respectively. This thus answered the

that whether an independent variable was significantly correlated

dependent variable or whether an independent variable had a

nt contribution to the dependent variable in a regression model. If

for a regression coefficient was very small, a null hypothesis was

claiming that the contribution from the corresponding

ent variable to the dependent variable was significant.

(a) (b)

.9. The significance of a regression coefficient in two regression models.