The word regression is a noun. It cannot be an adjective. When it is paired with another noun, it is a noun adjunct.
Examples:
"In statistics, regression analysis refers to techniques for modeling and analyzing several variables"
"Regression techniques are used by psychologists."
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of, pertaining to, or determined by regression analysis: regression curve; regression equation. dictionary.com
Regression testing is something every programmer should do after changing the code. Elderly individuals sometimes undergo a remarkable regression to a childlike state. The military's observers reported the regression of the country to a feudal state.
Both. It just matters how you use it in the sentence.
Prodigious is not a verb, it is an adjective. You can tell just by looking at him that his ego is prodigious.
My dictionary said plus is a noun, an adjective, a preposition and a conjunction but not a verb.