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The phrase "on the response" is correct and usable in written English.
It can be used when referring to something that is contingent upon or related to a response given by someone.
Example: "We will make our decision on the response we receive from the committee."
Alternatives: "regarding the response" or "based on the response."
Exact(60)
Figure 4 displays the effect of slope angle on the response with depth.
"It depends entirely on the response".
I worked on the response to the Pakistan floods.
Gay mostly demurred on the response with a simple "No".
The day after the concert, Zehetmair reflects on the response.
It depends on the response of the taxi industry.
The study includes the earthquake spatial variability on the response.
The refractive index depends on the response of a material to electric and magnetic fields.
By e-mail, I polled old schoolmates on the response in the province to Paisley's retirement.
Rogers, not to be outshouted, copied Dmitry's classmates on the response.
A year on the response – or lack thereof – is as astonishing as it was expected.
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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