Results of a regression may show that something-is-the-case.
A (kernel regression) can be an estimate of a conditional mean of residuals.
A test may use a (kernel regression estimate) of a conditional mean of residuals.
A statistical significance may pertain-to (regression coefficients).
(Regression models) can be for a purpose of adjusting for change.
Hedonic regressions can be for components of (consumer price indices).