1. Appropriate Regression Analysis?

Does this even make sense?

Am told to do a multiple regression analysis. The response variable and the explanatory variables add up and should give a percent of the total product. Example:
Milk = water + fat + protein + e ~= 96% (all are in terms of percentages, 96% is the average total from the dataset)
where e is the error such that e~NID(o,sigma)
The regression I was asked to do is
protein = β + water*x1 + fat*x2 + e
We want this so we can calculate protein without having to measure it (data is from some test samples)
This to me makes absolutely no sense...Since the equation is just
protein = -water-fat-e +100
so the coefficients should be negative 1 and beta = 100???
Would it be more appropriate to do a hypothesis test as such:
Protein + Water + Fat ~= 96% of total milk weight (the total average is the average from data)

Hypothesis test:

H0 := (Water + Fat) - Protein = 45.1 (average difference obtained from data)
H1 := (Water + Fat) - Protein != 45.1

Not sure what analysis would be best and any help would be most appreciated. Thanks!

2. Re: Appropriate Regression Analysis?

i dont really understand your post im afraid, but it sounds like you have multicollinearity and/or errors that are correlated to your explanatory variables.

But its hard to say as you have written Milk ~= 96% which i cant really interpret at all.

3. Re: Appropriate Regression Analysis?

Sorry for being unclear. ~= is supposed to mean approximately equal to, maybe just ~ would be more clear but that seemed confusing with having a distributiuon.