Functional form

A 2×2 matrix organises the four regression functional forms by whether X and Y each enter as a level or a logarithm. The level–level cell reads β₁ units in Y per 1-unit rise in X; level–log reads β₁/100 units in Y per 1% rise in X; log–level reads approximately 100β₁% change in Y per 1-unit rise in X; and log–log reads β₁% change in Y per 1% rise in X, which is a direct elasticity. The same printed coefficient number carries a completely different economic meaning depending on which cell of the matrix applies.