Which Gospel was written by a doctor?
Here is more information about Luke from the Open Bible:
“The ‘we’ portions of Acts reveal that the author was a close associate and traveling companion of Paul. Because all but two of Paul’s associates are named in the third person, the list can be narrowed to Titus and Luke. Titus has never been seriously regarded as a possible author of Acts, and Luke best fits the requirements. He was with Paul during his first Roman imprisonment, and Paul referred to him as “Luke the beloved physician.” During his second Roman imprisonment, Paul wrote “Only Luke is with me,” an evidence of Luke’s loyalty to the apostle in the face of profound danger.
Luke may have been a Hellenistic Jew, but it is more likely that he was a Gentile. It has been suggested that Luke may have been a Greek physician to a Roman family who at some point was set free and given Roman citizenship. Another guess is that he was the “brother” referred to in 2 Corinthians 8:18-19. Ancient traditions strongly support Luke as the author of Luke and Acts. Tradition also says that Luke was from Syrian Antioch, remained unmarried, and died at the age of eighty-four.”