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I want to create a model in a food processing plant where my dependent variable is Electricity (KWhr) consumption per kg. Plant produce different food items with varying electricity consumption. I'm interested in knowing the impact of the proportion of each food item on consumption per kg. so my model is

 consumption per kg produced (Kwhr/kg) = alpha0 +alpha1(Food Item A/Total Production) + 
                                     alpha2(Food Item B/Total Production)+....+Other variables

Is it correct to frame the question like this?. I have Total Production on both sides of the equation as the denominator. What is the right way to approach this problem?. I would like to hear your thoughts on this. Any help is highly appreciated.

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Energy is additive but energy-per-kg is not.

Assume

$p_i$ be the energy consumption rate for food $i$ ($\mathrm{kJs^{-1}} = \mathrm{kW}$),

$t_i$ be the # second for producing 1 kg of food $i$ ($\mathrm{skg^{-1}}$)

$w_i$ be the amount of food $i$ produced ($\mathrm{kg}$)

so $p_it_iw_i$ will give us the total energy consumption for food $i$

Consequently,

$E = \sum_i p_it_iw_i + C $

$E$ is the total energy consumed, and $C$ encapsulate other energy consumption independent of the food.

For energy consumption per kg,

$E' = \frac{\sum_i p_it_iw_i + C}{\sum_i w_i} $

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  • $\begingroup$ how does it impact my model approach? Can you elaborate? Thanks for your reply $\endgroup$
    – NAS_2339
    Commented Feb 9, 2022 at 6:32
  • $\begingroup$ Your model seems to add up Food_A's consumption-per-kg, Food_B's consumption-per-kg, and so on. I think it's not correct because you cannot add them to get the total consumption-per-kg. E.g. Tom spends \$2 to earn \$5, Peter spends \$3 to earn \$21. In total they spend \$5 to earn \$26, so the total return-on-investment(ROI) is \$26/\$5 = 5.2. However, ROI of Tom alone is 2.5, ROI of Peter along is 7, the sum of these two ROIs is 9.5 and it is not the total ROI. $\endgroup$
    – Raymond Kwok
    Commented Feb 9, 2022 at 6:50
  • $\begingroup$ Thanks for the reply. I'm using the percentage contribution of Food_A and Food_B as features, not consumption per kg. If my total production is 100 Kg, of which Food_A is 70 and Food_B is 30, my features will be 0.7 and 0.3, respectively. I think this is different from the scenario you described. Am I missing something? $\endgroup$
    – NAS_2339
    Commented Feb 9, 2022 at 7:05
  • $\begingroup$ I think this does not change the game. Again in the example of Tom and Peter, Tom spends \$2 to earn ($5/26=$) 19.2% of the money and Peter spends \$3 to earn ($21/26=$) 80.8% of the money, and the rest of the story remains the same. $\endgroup$
    – Raymond Kwok
    Commented Feb 9, 2022 at 7:08
  • $\begingroup$ 5.2 becomes $5.2/26$. And 2.5 and 7 become $2.5/26$ and $7/26$ respectively and the later two do not add up to the first number. We are just dividing everything by 26. $\endgroup$
    – Raymond Kwok
    Commented Feb 9, 2022 at 7:22

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