The National Weather Service in 1990 published the following multiple regression equation for Heat Index (HI) relative to the ambient temperature (T) and the relative humidity (RH)
\begin{equation*}
H = -42.379 + 2.04901523 \cdot T + 10.14333127 \cdot R - 0.22475541 \cdot T \cdot R \\ - 6.83783 \cdot 10^{-3} \cdot T^2 - 5.481717 \cdot 10^{-2} \cdot R^2 + 1.22874 \cdot 10^{-3} \cdot T^2 \cdot R \\ + 8.5282 \cdot 10^{-4} \cdot T \cdot R^2-1.99 \cdot 10^{-6} \cdot T^2 \cdot R^2.
\end{equation*}
Notice, their model utilizes quadratic terms and therefore uses a generalization of the linear result presented above. Details on how this equation was determined and other details are available at https://www.wpc.ncep.noaa.gov/html/heatindex_equation.shtml .