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The phrase "a simple relationship but" is correct and usable in written English.
It can be used to introduce a contrast or complication in a discussion about a relationship that is otherwise straightforward.
Example: "It's a simple relationship but there are underlying complexities that we need to address."
Alternatives: "a straightforward relationship yet" or "an uncomplicated relationship however".
Exact(2)
We present nine themes that capture the links and spaces between design and scenarios, yet suggest that they are not a straightforward overlap or a simple relationship, but rather a range of interactions between the fields, including feeding in, bridging, tension and repulsion.
The depressive symptom reporting at 14 years of age in the 47% of the cohort exposed to some type of childhood adversity did not follow a simple relationship but did show clear-cut gender differences.
Similar(58)
Much was made about it because of her father and whatnot, but we had a simple relationship in my opinion.
This suggests that the level of damage has a significant effect on mortality but there is not a simple relationship with SDI score (i.e. log-linear).
A simple relationship for DR is derived.
Mr. Papillaud described his deal with Roseburg as a simple relationship between a buyer and seller.
Investigators should now appreciate that the force-calcium relationship is not a simple relationship.
A simple relationship between viral load and survival time in HIV-1 infection.
There is a simple relationship between the make code and break code.
Unfortunately, there does not appear to be a simple relationship between rainfall and counts of sewage-indicating bacteria, said O'Mullan.
A simple relationship is derived for an estimate of the average particel size.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com