# what is strong correlation?

Suppose I have a a vector of correlations between the target and the variables:

   0.550740873  0.392085002  0.366500158  0.323678671  0.287849277  0.087884394  0.058511638
 -0.001433074 -0.043025966 -0.160413561 -0.250894036 -0.271016826 -0.278879869 -0.303903240
 -0.304250965 -0.340604136 -0.461963084 -0.462235863 -0.485940670 -0.666877216


I'd like to know, which of the variables, out of the ones I have, have a strong relationship with the target.

Just to clarify, I know what correlation means intuitively and mathematically. For instance, I know that if correlation is 1, it's strongly positive, and if it's -1, then it's strongly negative, and anything in between [-1,1] would be slightly less correlated.

My attempt to answer this question would be to calculate the mean of the absolute values of these correlation coefficients, which is 0.3. And so, I would say that every variable which has correlation higher than 0.3 or lower than -0.3 would qualify for a "Stronger than average relationship with the target variable".

Would this be wrong to do?

The correlation coefficients that you shared do not bear the information about sample size (the degrees of freedom of your possible model). It may be that all of the independent variables have insignificant correlation to the target.

1. I propose you make a statistical test with null hypothesis stating that the correlation coefficient is not different from zero in population.

In R this can be accomplished by using function cor.test() which takes two vectors corresponding to your independent and dependent variables. Then you proceed by looking at the test's statistic or p-value, following a regular logic of making statistical hypothesis checking.

Significantly associated pairs of variables will have, say, test statistic of the absolute value of 3 or more (that depends on what value of the significance level you had to choose prior to testing).

1. An additional step could be to compare the correlation coefficients in terms of their difference measuered again as a standard error, not as they are. However, to make this, you can probably have to run some calculations manually.

Note that, depending on the type of correlation method, e.g., Pearson's, you can only make statements about the relationships in a linear sense.

• Thank you for your answer, appreciate it. I have done these, and now I have 19/20 which are significantly associated with the outcome variables, and also I have big test statistics. How do I determine whether they have strong relationships? I mean, how does one variable qualify for a "strong" relationship? Is this subjective? As in I can just say the "top 3" strongest are such and such variables?
– user255658
Jan 29 at 22:27
• It is rather subjective to name the strong ones. Try top N strongest. Another option is to cluster a vector of coefficients in three groups (k means, for example). It will split the vector into strongest, medium, and weak. Jan 30 at 6:30