Hmmm.
According to the new Familysearch web site (I just hate[/b] it compared to the old IGI, but I can't access the old site today for some reason)
John Anderson and Elizabeth Fraser were married in the parish of Urray, Ross and Cromarty, on 7 June 1861 and had
Ann, born 20 September 1863
Robert, born 7 April 1865
William, born 16 June 1867 died 17 June 1867
William, born 30 May 1869
John, born 17 May 1872
all in Inverness. And yes, John's age is 4 years 'out' compared with his death certificate.
There are also listings for
Christina, born Glasgow 10 May 1869
Abbina, born Greenock 10 May 1869 (yes, the same day, just 3 weeks before William)
but these two are 'submitted' so can safely be ignored.
In the 1881 census the only possible John A is a boarder in the household of Duncan Fraser at Lagnalion, Inverness, but I have not found any of the other children yet.
Edward Reeves, street singer, aged 31, born England, and Margaret Reeves, 29, born Kirkcaldy, are among numerous lodgers at 65 Grassmarket, Edinburgh. The CD transcription does not say whether either or both was married. The index at SP lists one match for a marriage of Edward Reeves to an Elizabeth A* in 1883, but the bride's surname is apparently neither Fraser nor Anderson.
You might find it useful to get these two marriage certificates from SP and see what they reveal.