TLDR: When performing a simple linear regression, if you have any concern about outliers or heterosedasticity, consider the
TheilSen estimator
.
A simple linear regression estimator that is not commonly used or taught in the social sciences is the TheilSen estimator. This is a shame given that this estimator is very intuitive, once you know what a slope means. Three steps:
 Plot a line between all the points in your data
 Calculate the slope for each line
 The median slope is your regression slope
Calculating the slope this way happens to be quite robust. And when the errors are normally distributed and you have no outliers, the slope is very similar to OLS.^{1}
There are several methods to obtain the intercept. It is reasonable to know what your software is doing if you care for the intercept in your regression. TheilSen regression is available in two R packages I know of: WRS
^{2} and mblm.
mblm
includes a modification to Theil’s original method that has a higher breakdown point (more robust).^{3} This modification is the default method.
WRS
contains two functions for TheilSen regression: Theil’s original method in the tsreg
function, and a modification for small samples when there are tied values in the outcome in the tshdreg
function.
Re my comment at the top regarding TheilSen for simple linear regression when there are concerns about outliers and heteroskedasticity, see Dietz^{4} and Wilcox^{5} below.
I conducted a toy simulation to see how TheilSen competes with OLS under heteroskedasticity; It is the more efficient estimator.

Wilcox, R. R. (1998). A note on the TheilSen regression estimator when the regressor is random and the error term is heteroscedastic. Biometrical Journal, 40(3), 261–268. doi: 10.1002/(SICI)15214036(199807)40:3<261::AIDBIMJ261>3.0.CO;2V ↩︎

Wilcox Robust Statistics  Rand Wilcox’s collection of robust methods. It is not available on CRAN, as CRAN requires proper documentation for all functions. This is a good set of installation instructions  https://web.archive.org/web/20170712140359/http://www.nicebread.de/installationofwrspackagewilcoxrobuststatistics/. ↩︎

Siegel, A. F. (1982). Robust regression using repeated medians. Biometrika, 69(1), 242–244. https://doi.org/10.1093/biomet/69.1.242 ↩︎

Dietz, E. J. (1987). A comparison of robust estimators in simple linear regression. Communications in Statistics  Simulation and Computation, 16(4), 1209–1227. https://doi.org/10.1080/03610918708812645 ↩︎

Wilcox, R. R. (1998). A note on the TheilSen regression estimator when the regressor is random and the error term is heteroscedastic. Biometrical Journal, 40(3), 261–268. ↩︎
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