Question

CAN SOMEONE PLEASE HELP ME WITH THIS PROPORTIONALITY QUESTIONS!!!?!?

Answer 1

The question is not so clear as to what "roughly proportional" means but we will try to deduce the relationship by simple linear regression. Two cases will be used, its either the sugar content is directly proportional to the caloric value or an inverse relationship is present. This can be easily done using MS excel.

let y = caloric value
x- sugar content

For direct proportionality

y = kx 

for inverse relationship 

y = k/x

the measure here is the r^2 (i forgot the proper statistical term) in which a value closer to 1 would mean that the expression gives a model which describes the proportionality of the data.

I tried using the linear relatioships but both did not get satisfactory results.
However, I tried fitting the data in a 2nd order polynomial and the result is good, in fact the r^2 is 1. Use the MS excel to do this. 

the equation to describe the relationship is

y (calories/mL) = 504.67x^2 - 53.002x + 1.3003

however please be casreful in using this relationship since some values of x (sugar content) will yield negative values. It'll be best to try another model (logarithmic or exponential)