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"higher by" is a perfectly acceptable phrase to use in written English
It is typically used to describe a comparison of two different values or amounts, with one being greater than the other by a certain amount. For example: "Sales of the product increased higher by 10% compared to the year before."
Exact(59)
Sales were driven higher by strong demand for home furnishings.
'They're higher by about 30percentnt,' he says.
Stewart is higher by 13.2%.
eHealth is higher by 14.25%.
Westlake is higher by 10.3%.
Steelcase is higher by 10.25%.
Kraton is higher by 11%.
Essex is higher by 1%.
Affymax is higher by 21.6%.
Trintech is higher by 25.4%.
Fortinet is higher by 19.5%.
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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