¥Test for Significance of Linear Regression
HThis is done by testing
whether additional parameters significantly improve the fit
åFor simple case
H Y = b0 + b1X1 + e
å
H0: b1 = 0
å
H1: b1 0
åFor general case
å
Y =b0 + b1X1 +
b2X2 +
É,+ bq-1Xq-1 + bqXq +
É + bp-1Xp-1 +
e
å
H0: bq = bq+1 = ...
= bp-1 = 0
å
Ha: bk 0, for some k, q ² k ² p-1
å
åFreg is the F-statistic for determining if Full model significantly
improved on the
reduced model
íNOTE: This F-statistic is assumed to have a central F-distribution.
This is not the case when there is a lack of fit
¥