If we did a poll asking what is most characteristic and / or name of the famous British detective Sherlock Holmes, without a doubt, the phrase "Elementary, my dear Watson" would be among the most responded. 

But ... did you know that in any of the novels written by Sir Arthur Conan Doyle adventures of the protagonist says at one point that hose? 

Yes it is correct that Sherlock Holmes, on occasion (not always) pronounces the word "elementary" and other "my dear Watson", but separately and in different contexts, never together. 

The first time it appeared the famous phrase 'Elementary, my dear Watson "was in a 1939 film (nine years after the death of Conan Doyle) entitled The Adventures of Sherlock Holmes. From there it became popular, being used in many feature films, series and new adventures written by other authors.