  Context. In order to understand galaxy evolution, it is essential to measure
star formation rates (SFRs) across Cosmic times. Aims. The use of radio
continuum emission as an extinction-free star formation tracer necessitates a
good understanding of the influence of cosmic-ray electron (CRE) transport that
we are aiming to improve with this work. Methods. We analyse the spatially
resolved radio continuum-star-formation rate (radio-SFR) relation in 15 nearby
galaxies using data from the LOw Frequency ARray (LOFAR) and the Westerbork
Synthesis Radio Telescope (WSRT) at 144 and 1365 MHz, respectively. The hybrid
SFR maps are based on observations with Spitzer at 24 $ {\mu}$m and with GALEX
at 156 nm. Our pixel-by-pixel analysis at 1.2 kpc resolution reveals the usual
sublinear radio-SFR relation for local measurements which can be linearised
with a smoothing experiment, convolving the hybrid SFR map with a Gaussian
kernel that provides us with the CRE transport length. Results. CRE transport
can be described as energy-independent isotropic diffusion. If we consider only
young CREs as identified with the radio spectral index, we find a linear
relation showing the influence of cosmic-ray transport. We then define the CRE
calorimetric efficiency as the ratio of radio-to-hybrid SFR surface density and
show that it is a function of the radio spectral index. If we correct the
radio-SFR relation for the CRE calorimetric efficiency parametrised with the
radio spectral index, it becomes nearly linear with a slope of $1.01\pm 0.02$
independent of frequency. Conclusions. The corrected radio-SFR relation is
universal and holds, both, for global and local measurements.
