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"Based on the observation" is a correct and usable phrase in written English.
It can be used to introduce the reasoning or evidence for a statement or conclusion. Example: "Based on the observation of their behavior, I can confidently say that they are not getting along."
Exact(60)
Based on the observation of [13], several advancements have been proposed later [15, 16].
Based on the observation of the temperature record, most of the years were normal.
Based on the observation of Theorem 2.2, we have the following.
Based on the observation, the depression was upgraded to tropical storm status and given the name Francelia.
Based on the observation of the ROC curve, we also showed that the MNA is accurate.
According to the chapter notes, this conclusion is based on the observation of one friend of the Kennedy family.
A7 Assessment Centers This method is based on the observation of behaviors conducted by trained observers.
Thus, at just glance, our approach (based on the observation of behavioral transformations) seems like the only reasonable one presently.
(P.T.S.D. is assessed on a number of scales, some subjective and others based on the observation of the clinician).
Darwinian theory is based on the observation that evolution selects for success: animals with traits that promote survival or reproduction pass on their genes; others die out.
This model is based on the observation and feedback factors.
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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