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The phrase "analysis backs this up" is correct and usable in written English.
You can use it when referring to data or findings that support a particular claim or argument.
Example: "The research findings are compelling, and the analysis backs this up, demonstrating a clear correlation between the two variables."
Alternatives: "analysis supports this" or "analysis confirms this."
Exact(1)
Historical reports suggest a major quake shook the Myanmar region in 1762, and Cummins's analysis backs this up.
Similar(59)
I haven't seen any cost-benefit analysis backing this up, and, frankly, I don't think such concerns are driving the debate.
The new analysis backs up that claim.The purpose, say the researchers, is not to lambast individual doctors for squandering scarce public money.
The sensitivity analysis backs up the findings.
But the researchers' numbers suggest that as many as a fifth of the internal conflicts of the period were affected by El Niño.Further analysis backs up the idea.
We present theoretical analysis backed up by experimental results, showing that the proposed solution outperforms popular decentralized infrastructures for web discovery, Chord (and some of its successors), BATON (and it's successor) and Skip-Graphs.
Whatever the affiliation or funding source, both of these reports should be dismissed as merely the unsubstantiated opinions of a few academics, as opposed to reliable scientific analysis backed up by peer review.
Third, a hypothesis-free pathway analysis, backed up by additional text-mining, was employed in the secondary filtering of potential candidate genes to reduce bias.
Second, local governments readily accept social indicators on the quality of life (QOL) as a development agenda, after undergoing a situation analysis backed up by research.
Imison backed this up.
Research backs this up.
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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