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Data analysis when much more columns than rows

Hello everybody
I would like to ask for your help because I have a data set with:

in columns, process parameters of a galvanized steel production line
in rows, coils that have been processed on this production line

The objective is to correlate a quantity of defects appearing on a coil to one or several process parameters.
Unfortunately, I have a data set with many more columns (407) than rows (63).
Do you have any advice on how to proceed?

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