Simple CORRELATION query

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hi. i am analysing my data using a correlation matrix, and then multiple regression. I have noticed that some of my correlation co-effecients are 0.18 and 0.24, meaning little linear relationship. Dont those variables have to be dropped for the regression equation?. Prior studies have had the same correlations ad me, but just said there is a 'weak correlation' between he variables, and continued straight onto the regression, why is this?

also if a correlation coeffecient is 0.18 but significant what does this mean?



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They don't necessarily need to be dropped - it depends on whether they are significantly larger than 0 (no correlation) and whether it makes sense from a theoretical standpoint (outside of statistics). In some fields, they are thrilled with anything above 0.10, and other fields, anything below 0.90 is useless.

If r=.18 is significant, it means that it is larger than 0 and probably not due to chance (there is an actual linear relationship, but it is pretty weak).