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I have a graph with 2 plots (Plot A and Plot B, both are lines), plot A has a lower y-intercept and also lower slope than plot B. How do I represent this difference in one numeric value? Source: I am doing an experiment to compare 2 different power settings on a computer. This is a Power Vs Performance plot where lower the y-intercept and lower the slope the better. So in order to represent the difference between the 2 settings I need to come up with 1 numeric value that indicates this difference. (The most obvious would be a ratio of slopes of both the lines but that does not include the difference in y-intercepts. )

AcidBurn
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  • I suggest using the area under the line between two end points. One would likely be $x=0$. Where the other would be is your choice. Probably the highest point you've plotted. The area under $y=mx + b$ between $x=0$ and $x = x_1$ is $x_1(\frac m2x_1 + b)$. – Paul Sinclair Aug 17 '17 at 22:56
  • @PaulSinclair, thanks for the reply. If the plots are a curve and not a straight line how will this formula change? – AcidBurn Aug 21 '17 at 16:23
  • The area under a curve is given by its integral. For a line, this reduces to the formula I gave above. For more complex curves, you'll need to bring in calculus. But the area under the curve is almost certainly the best measurement you can use for your purpose. – Paul Sinclair Aug 21 '17 at 23:41
  • The integral is easy to use when you know the equation of the curve. But is there a way by which you can find the equation of an irregular curve? – AcidBurn Aug 21 '17 at 23:53
  • That depends on what information you have about the curve. For instance if you have $n$ points the curve passes through, and you know the curve is a polynomial of degree $n-1$ or less, then it is easy to figure out what the polynomial has to be. But if you only assume that the curve is a polynomial, then the polynomial produced this way is usually an extremely poor choice, swinging wildly between the known points. If all you know about the curve is the points and that it is continuous, consider it piecewise linear. If you know the curve is smooth, use a cubic spline. – Paul Sinclair Aug 22 '17 at 16:17

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