# The length of explanatory vectors in CCA and their relation to impact on (explained) variance

#### zwergje

##### New Member
I performed CCA on a taxa-sample matrix using 8 explanatory variables. They say that the length of the vectors that represent the explanatory variables in your triplot visualization is proportional to their impact on the taxonomic variance. However, since various of my explanatory variables have a similar length, I prefer to calculate their length using the CCA score list above visual estimation.

The problem: I calculated the root of the sum of squares of all 8 CCA scores of the explanatory variables. However, it turns out that the lengths of the explanatory variables equal the root of the sum of squares of only CCA scores of the first two (canonical) axes in the graph. As a result, I have two vectors in my graph of which the smallest is almost half of the bigger one, while when I calculate their length by taking the square root of the sum of the squares of their CCA scores (over al 8 canonical axes):
Precip -0,1315 0,074613 -0,00788 -0,40556 0,077369 0,144983 0,021653 -0,04012
Open area -0,23588 0,144588 0,18441 -0,09637 -0,01802 0,174098 -0,25398 -0,02785

Result 1: length of resp. Open area over all 8 (canonical) dimensions 0,465282326 0,464494416

Result 2 length of resp. Precip over the first 2 (canonical) dimensions.: 0,151190429 0,276666081

That seems strange: the lengths of the vectors actually only represents the impact of the explanatory variables over the first two (strongest) canonical axes it seems. As a result, the impact given to precipitation is much smaller as when all 8 dimensions are included.