No. If Factor X is correlated to Factor Y then you can use one as a predictor of the other, but you should never assume that one causes the other (it may, but correlation alone doesn't prove it).
Consider the correlation between proximity to a swampland and chances of contracting malaria. Do swamplands cause malaria? No. Malaria is propagated via mosquitoes which of course love to live in swamplands. So your proximity to a swampland is a useful predictor of your chances of contracting malaria, but doesn't cause it.
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No! Correlation by itself is not sufficient to infer or prove causation.
If anxiety and depression are correlated, there are three possible directions of causality. These are anxiety causes depression, depression causes anxiety, and there is an environmental stimuli that causes both anxiety and depression.
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If measurements are taken for two (or more) variable for a sample , then the correlation between the variables are the sample correlation. If the sample is representative then the sample correlation will be a good estimate of the true population correlation.
Evidence that there is no correlation.