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I have two variables. There is a statistically significant correlation between the two (spearman coefficient 0.82, p<0.01). But the dependent variable can be either positive or negative (the trendline crosses 0).

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How do I describe this in text? I want to be able to say that a higher independent variable (x axis) value correlates with a positive dependent variable (y axis), and a lower independent variable correlates with a negative dependent variable. But it feels like this this needs further qualification or additional statistical analysis to establish?

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When $X$ is high, $Y$ tends to be high; when $X$ is low, $Y$ tends to be low. This is the usual way correlation works.

The trend line crossing $0$ has no bearing on the correlation. You might be confusing that with a confidence interval for the correlation, which is a different concept, and you are right that a confidence interval containing $0$ corresponds to being unable to reject a null hypothesis of being equal to $0$. (But, again, that is a different concept.)

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  • $\begingroup$ Thank you! The fact that Y tends to be a negative value when X is low, and Y tends to be positive when X is high; this is a relevant finding though, beyond Y being only higher or lower. The Y value is the change in a certain metric, upon a certain intervention. Would it be accurate to say: "when X is high, Y tends to increase post-intervention; when X is low, Y tends to decrease post-intervention; the x-intercept is at 28.6"? $\endgroup$ – ericthewoollymammoth Jan 12 at 3:34

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