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How can you have significant correlations and insignificant coefficients?

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I'm a psychology graduate, so I admit that statistics do not come naturally to me. However, I find them fascinating nonetheless.

At the moment i'm struggling with regressions, or specifically in this instance a multiple linear regression.

I was just curious about the relationship between correlations and coefficients. In my assignment we've been asked to look at some data pertaining to stress (all made up, of course!) and the results indicate that several of the factors correlate to one another (e.g. assignment anxiety and social coping skills),as would be expected. However, only a single coefficient is significant in relation to the outcome variable (stress).

I'm sure this is probably a ludicrously easy thing to understand but as no one has explained it to me I feel lost about how these two things (correlations and coefficients) are related (if at all they are).


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