
338 Data Analysis and Statistics for Geography, Environmental Science, and Engineering
The strength of the linear relationship between independent variables X
1
and X
2
is collinearity.
More specically, X
1
and X
2
are perfect collinear if all pairs of observations are linearly related
aaXaX
01122
0
(10.25)
Then, high correlation between X
1
and X
2
implies strong collinearity. When we have several
independent variables, we can have multicollinearity among these variables. More speci-
cally, there is perfect multicollinearity if there is a linear relationship among some of the inde-
pendent variables
aaXaXaX
ii kki01122
0
(10.26)
Thus, high ...