Question: Is there any evidence that collinearity causes some predictors in this model to be insignificant?
Using R, I calculated the correlations of the predictor variables of a linear model.
lcavol lweight age lbph svi lcp gleason pgg45
lcavol 1.00 0.19 0.22 0.03 0.54 0.68 0.43 0.43
lweight 0.19 1.00 0.31 0.43 0.11 0.10 0.00 0.05
age 0.22 0.31 1.00 0.35 0.12 0.13 0.27 0.28
lbph 0.03 0.43 0.35 1.00 -0.09 -0.01 0.08 0.08
svi 0.54 0.11 0.12 -0.09 1.00 0.67 0.32 0.46
lcp 0.68 0.10 0.13 -0.01 0.67 1.00 0.51 0.63
gleason 0.43 0.00 0.27 0.08 0.32 0.51 1.00 0.75
pgg45 0.43 0.05 0.28 0.08 0.46 0.63 0.75 1.00
I thought that there is a relatively strong correlation between lcp and lcavol, lcp and svi, lcp and gg45, gleason and gg45.
Would a correlation value of >0.5 be considered a strong correlation (ie: one of the variables would do a good job of representing the other)? How do we determine the minimum benchmark for when two variables have a strong correlation?