Transportation Statistics and Microsimulation

Linear Regression    ◾    199

10.8.1 Confidence Intervals on Regression Parameters

Condence intervals can be calculated for the k (= p + 1) regression param-

eters (including the intercept) using the formula

ˆ

(/,)

,/

βα

α

j

tnkt

nk

±− −

−−

12

12

(10.24)

More advanced textbooks, such Johnson and Wichern (2007), give formulas

for condence ellipsoids. Condence ellipsoids give joint condence regions

for the p-estimated regression parameters that have a minimum area.

10.8.1.1 Extrapolation

It is extremely dangerous to use predictors outside of the joint range of

experimental data. For observational studies where data are typically col-

linear, this is ver