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We present a method to self-consistently propagate M$_{*}$ and SFR ($\Psi$)uncertainties onto intercept, slope and intrinsic scatter estimates for asimple model of the main sequence of star forming galaxies where $\Psi = \alpha+ \beta$M$_{*} + \mathcal{N}(0,\sigma)$. From simple idealised models set upwith broad-band photometry from NIRCam filters at $z\sim5$, we test the methodand compare to methods in the literature. Simplifying the $\Psi$ estimate bybasing it on dust-corrected MUV can help to reduce the impact of template setdegeneracies on slope and intercept estimates, but act to bias the intrinsicscatter estimate. We find that broad-band fluxes alone cannot constrain thecontribution from emission lines, implying that strong priors on theemission-line contribution are required if no medium-band constraints areavailable. Therefore at high redshifts, where emission lines contribute ahigher fraction of the broad-band flux, photometric fitting is sensitive to$\Psi$ variations on short ($\sim$ 10 Myr) timescales. Priors on age imposedwith a constant (or rising) star formation history (SFH) do not allow one toinvestigate a possible dependence of $\sigma$ on M$_{*}$ at high redshifts.Delayed exponential SFHs have less constrained priors, but do not account for$\Psi$ variations on short timescales, a problem if $\sigma$ increases due tostochasticity of star formation. A simple SFH with current star formationdecoupled from the previous history is appropriate. We show that, for simpleexposure-time calculations assuming point sources, with low levels of dust, weshould be able to obtain unbiased estimates of the main sequence down tolog(M/M$_{\odot}$) $\sim$ 8 at $z\sim5$ with the James Webb Space Telescopewhile allowing for stochasticity of star formation.

Modelling the M*-SFR relation at high redshift: untangling factors driving biases in the intrinsic scatter measurement