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I have several curves in one graph (see fig.). There are 5 discernible segments within each
curve that are individual slopes. Within each "x-coordinate segment" there are five samples with their respective individual slopes.

If the slope of one sample is steeper than the other ones then you can read from it that it has a greater contribution than the other slope regarding increase with respect to the cumulative values of the individual curves.

Now have a look at the red curve: Between segment "temperature °C" 3 and 4 the slope appears to be much steeper than the respective segments of the blue and black curves (latter colors have no meaning here).

Now, after elaboration of the graph I would like to calculate the steepness of the segment of the curve with respect to the corresponding segments of the other curves but account for the contribution to the steepness by the cumulative (total) values.
enter image description here

I did the calculation of contribution for segment 3-4 of the red curve like this: 

1.48*1.48/4.41 

with   1.48 difference temperature °C 4 minus 3 and
       4.41 as cumulative temperature of all curve segments

I don't know if I calculated this correctly?! So, did I? (In the end-effect I would like to know if higher cumulative values have a steeper curve in this exact segment 3-4, i.e. do a correlation of it with the cumulative values)

behold
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Vera Marya
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1 Answers1

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I'm not sure I understood exactly the question, so sorry if I'm overcomplicating.

From what I understood, you have several components $j$ and you can compute the slope of each of them $m_j$: $$m_j = \frac{C_j(T_H) - C_j(T_L) }{T_H - T_L}$$ where $C_j(T)$ is the contribution of component $j$ at temperature $T$ that can be the higher temperature $T_H$ or the lower temperature $T_L$.

If you want the overall slope $m$, you need to consider the sum of the contributions of all components, so $$m = \frac{\sum_k C_k(T_H) - C_k(T_L) }{T_H - T_L}$$ I used a different letter $k$ for the components trying to avoid confusion of the formulas below.

Hence, the relative contribution of component $j$ to the overall slope is $$\frac{m_j}{m}$$

Since we are considering always the same temperature interval, $$\frac{m_j}{m} = \frac{C_j(T_H) - C_j(T_L) }{\sum_k C_k(T_H) - C_k(T_L) } $$

Ertxiem - reinstate Monica
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