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We present the overall statistical results from the Robo-AO Kepler planetarycandidate survey, comprising of 3857 high-angular resolution observations ofplanetary candidate systems with Robo-AO, an automated laser adaptive opticssystem. These observations reveal previously unknown nearby stars blended withthe planetary candidate host star which alter the derived planetary radii ormay be the source of an astrophysical false positive transit signal. In thefirst three papers in the survey, we detected 440 nearby stars around 3313planetary candidate host stars. In this paper, we present observations of 532planetary candidate host stars, detecting 94 companions around 88 stars; 84 ofthese companions have not previously been observed in high-resolution. We alsoreport 50 more-widely-separated companions near 715 targets previously observedby Robo-AO. We derive corrected planetary radius estimates for the 814planetary candidates in systems with a detected nearby star. If planetarycandidates are equally likely to orbit the primary or secondary star, theradius estimates for planetary candidates in systems with likely bound nearbystars increase by a factor of 1.54, on average. We find that 35previously-believed rocky planet candidates are likely not rocky due to thepresence of nearby stars. From the combined data sets from the complete Robo-AOKOI survey, we find that 14.5\pm0.5% of planetary candidate hosts have a nearbystar with 4", while 1.2% have two nearby stars and 0.08% have three. We findthat 16% of Earth-sized, 13% of Neptune-sized, 14% of Saturn-sized, and 19% ofJupiter-sized planet candidates have detected nearby stars.

Robo-AO Kepler Survey IV: the effect of nearby stars on 3857 planetary candidate systems