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The phrase "are obviously based on" is correct and usable in written English.
It can be used when discussing the foundation or source of an idea, argument, or work, indicating that it is clear or evident.
Example: "The conclusions drawn in the report are obviously based on extensive research and data analysis."
Alternatives: "clearly derived from" or "evidently grounded in".
Exact(7)
In a sense, those works of his that are obviously based on previous music (like this one, Con Brio, composed as a tribute to Beethoven for the Bavarian Radio Symphony Orchestra) explode their models to create a soundscape of instability and unpredictability.
Both approaches are obviously based on available information: the literature-based approach needs that evidence for certain target groups can be obtained from review articles or original publications describing studies that have already been conducted in the research field of interest.
The dangerous defections are those that are obviously based on reason and logic.
Dressed up in their white-girl drag -- the celebutantes they are impersonating, the Wilson sisters, are obviously based on Nikki and Paris Hilton -- the Wayans brothers look as if they've just lumbered in from "Dawn of the Dead".
These published papers are obviously based on successful heating experiments.
All of the attacks are obviously based on the scientific findings of these geniuses, but also, it's probably the only opportunity we're going to have to see Stephen Hawking teleport through a worm hole to kick some ass. .
Similar(53)
When, during a comically botched-up getaway, a man is shot in the face, the image is obviously based on one of the most famous sequences in Eisenstein's "Potemkin," and the startled face is used the same way it was in "Potemkin" — to convey in an instant how someone who just happens to be in the wrong place at the wrong time, the irrelevant "innocent" bystander, can get it full in the face.
Logistic regression analysis revealed that unsupervised assignment of a child by hierarchical clustering to one of the four different BR patterns was obviously based on the same prediction factors in both independent datasets, i.e., age, to a much lesser extent duration of diabetes, and rarely sex.
The statement is obviously based on misinformation.
Kraus's "novel" was obviously based on her life.
His answers were obviously based on genuine knowledge.
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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