Uber, the ride-share company, uses R for statistical analysis. According to econometric analysis of DUI incidents (driving under the influence of alcohol or drugs) in Seattle, the introduction of the Uber service corresponded with a 10% decrease in DUIs (about 5 a week).
The analysis took account of day-of-week effects, plus a term for the introduction of legal marijuana in Seattle (which increased DUIs). It also compared results to DUIs in a "control" city (San Francisco) to rule out other macro-level effects.
CultureAmp, the "people intelligence platform", also uses R. In their cloud-based employee feedback application Murmur, R is to cross-validate the built-in analytics. R, and packages including relaimpo, is also used in research. You can see R results in these reports on Glassdoor data and the effect of managers on team commitment levels.
"R has enabled us as a small start up to compete with large global consultancies", says Jason McPherson, Chief Scientist at CultureAmp.