Allocating consumption to products Following scenario: Data from 12 truck companies is available. For each company the absolute value of diesel consumption is available. Each truck company can ship Product A, Product B and Product C – nothing else. Data for all companies is available in the form of:
X Units of Product A shipped
Y Units of Product B shipped
Z Units of Product C shipped
G Liter Diesel consumption in total of the individual company
Is it statistically possible to allocate Diesel consumption to the individual products? If it would only be two products it would be of course fairly simple to compute the values like this:
X/E = Diesel Consumption per Product A
Y/E = Diesel Consumption per Product B
Where E is the total amount of diesel Consumption by all trucking companies.
I wonder now if it is somehow possible to calculate correlations or something similar that allows the allocation of the total consumption to three different products with a certain confidence interval. Historic data from the trucking companies is also available.
I hope I expressed myself understandable. I am not exactly an expert in the field of statistics.
 A: Assuming each company ships a different amount of units over time, the historical data can be used to estimate this. If there is Company 1, 2, 3 and data for each month
Company Month Gas      X     Y     Z
1       Jan   100     10    20    30
2       Jan   1000   200   150   100
3       Jan   200     20    35    65
1       Feb   120     12    25    31
...
...

Then fit a linear model:
$$
G = \beta_0 + \beta_1X + \beta_2Y + \beta_3Z
$$
The coefficients of the linear model will represent the Diesel consumption for each unit of each product. For example, $\beta_1$ represents the average Diesel consumption for shipping each unit of Product A. Also, $\beta_0$ represents Diesel consumption not related to shipping products.
If there is reason to believe that each company has different amounts of Diesel consumption not related to shipping products, this can be represented by
$$
G = \beta_0 + \beta_1X + \beta_2Y + \beta_3Z + \beta_4 C_2 + \beta_5 C_3
$$
where $C_2$ is 1 if that row of data represents company 2 and is 0 otherwise. Now the Diesel consumption not related to shipping products for Company 1 is $\beta_0$ and for Company 2 is $\beta_0 + \beta_4$.
If there is reason to believe that Company 1 is more efficient than Company 2 at shipping Product A, look at
$$
G = \beta_0 + \beta_1X + \beta_2Y + \beta_3Z + \beta_4 C_2 + \beta_5 C_3 + \beta_6X C_2 + \beta_7 X C_3
$$
Now the Company 1's Diesel Consumption for shipping Product A is $\beta_1$ and Company 2's is $\beta_1 + \beta_6$
Make sure you're comfortable with the linear model's assumptions and you check for the model for a proper fit. There are also ways to determine which of the three nested models is most appropriate.
