Multiple driving factors

Although it's very convenient to express expected consumption as a straight-line function of a single identified driving factor, there are many cases where two or more factors determine the level of demand. These may be categorised as follows: Within your M&T spreadsheet or other software, a straight-line relationship would be expressed mathematically as a formula for E, the expected energy consumption:

E = k0 + k1.D -----------(1)

where D is the measured value of the driving factor (tonnes produced, or degree days, etc.) and k0 and k1 are constants unique to the process being monitored. If there are two or more driving factors D1, D2, D3, and so on, the expression for calculating expected consumption becomes

E = k0 + k1.D1 + k2.D2 + k3.D3 -----------(2)   See numerical example

Your M&T spreadsheet or other software should be able to handle this calculation perfectly well, once appropriate values of the constant k0, k1, k2, and so on have been found. Multiple regression analysis is one method of establishing these constants, and is a facility found in spreadsheet programs and the better kinds of dedicated M&T software.

Such a multi-driver target cannot be expressed diagramatically but it is possible to manipulate it to make it look like a single-factor target (which can then be shown as a two-dimensional scatter diagram). To do this one must decide which is the 'dominant' driving factor, and subtract from expected consumption the estimated effects of the remaining factors. For example, referring to equation (2), driving factor 2 can be assumed to account for k2.D2 units of consumption while driving factor 3 accounts for k3.D3 units. This expression...

(E - k2.D2 - k3.D3)

...represents expected consumption net of the effects of factors 2 and 3. For convenience we can call the expression E'. Rearranging equation 2 gives us...

(E - k2.D2 - k3.D3) = k0 + k1.D1 , or

E' = k0 + k1.D1 -----------(3)

Equation 3 has the same form as equation 1 and represents a straight line.

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