Answer:
This sentence would have to be corrected to:
According to Dr. James Peterman, it is extremely important to drink enough water every single day.
Explanation:
The last name in this excerpt, (Peterman), needed to be capitalized, as it was a proper noun. A proper noun is the name given to something to make it more specific.
The second part of the sentence need not be in quotes. Use quotation marks with <em>direct quotes</em>, with <em>titles of certain works</em>, to <em>imply alternate meanings</em>, and to write words as words.
The word "water" should not be in parenthesis. Parentheses are used to enclose incidental or extra information, such as a passing comment, a minor example or addition, or a brief explanation. The writer may choose to put additional information within parentheses or to set off the text using dashes or commas.