¥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
H 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 the 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
¥