I want to perform a quantile regression on two continuous variables; Y (DV) and X (IV). I want to find out if there is an significant association between Y and X.
When doing this in R like:
fit2 <- rq(Y ~ X,tau=c(.05, .25, .5, .75, .95))
If say, the 75% quantile of X is significant with a p-value < 0.05 but rest is not, can I say that X is significant in total? If none of the quantiles are significant, is X not significant in total?
Best Answer
As long as you correct for multiplicity (e.g. Bonferroni-Holm), this is one of many possible ways to test for association. Of course it can capture only linear aspects of the association. A non-significant result can thus be due to low power, lack of linear aspects in the true association or due to conservativeness of the correction for multiplicity.