Are 'by' in No. 1 and 'by' and 'according to' in No. 2 correctly used?

Are 'by' in No. 1 and 'by' and 'according to' in No. 2 correctly used?

1. A Japanese researcher told me that I was one of her respondents. She handed me a questionnaire, saying, "Please supply the needed data by writing your answer on the blank."

2. A Malaysian researcher told me that I was one of her respondents. She handed me a questionnaire, saying, "Please indicate your answer by putting a check according to the given response codes."