# logistic regression model when the correlation is insignificant

I'm new to statistics. I want to ask if i have two continuous variables with insignificant correlation between them, but when I converted one of them into binary outcome (according to its cutoff point) and it was entered to logistic regression model as a dependent variable and the other variable as independent variable (continuous) the P value was significant. is it possible? or in other words is it meaningful?

• Apart from "possible?" (yes) and "meaningful?" (quite possibly) you could add "useful?". Again, the short answer is quite possibly, but consider also information loss. For example, reducing height to tall and short compared with some threshold would be throwing away information we usually find interesting or useful. In your real example you need to be able to justify the "cutoff" and to be confident that a binary scale makes substantive sense. – Nick Cox Jan 6 '16 at 18:46

## 1 Answer

Assuming you're using Pearson's correlation coefficient $\rho$, note that $\rho$ only measures the strength of the linear relationship between your two variables. As such, an insignificant correlation between two variables does not indicate that there is no relationship between the two; merely that a linear relationship between the two variables does not exist.

As such, your $p$-value need not be called into doubt because of the insignificant $\rho$ value.

• thank you very much..what i understood is that we we can use the logistic regression in this case but not the linear regression? @Matt Brems – Reem M.Al Haj Jan 6 '16 at 17:52
• Yes, it seems as though linear regression is inappropriate in this case but that logistic regression is more appropriate. – Matt Brems Jan 6 '16 at 17:57