guess vs make an estimate of

guess

noun
  • A prediction about the outcome of something, typically made without factual evidence or support. 

verb
  • to suppose (introducing a proposition of uncertain plausibility). 

  • To solve by a correct conjecture; to conjecture rightly. 

  • To reach a partly (or totally) unqualified conclusion. 

  • To think, conclude, or decide (without a connotation of uncertainty). Usually in first person: "I guess". 

make an estimate of

How often have the words guess and make an estimate of occurred in a corpus of books? (source: Google Ngram Viewer )