Response Curve

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A Response Curve is a mathematical formula that converts an input value into an output value. It's comprised of a curve type and 4 variables.

Components

Curve Types

The curve types are:

  • Linear
  • Polynomial
  • Logistic
  • Logit
  • Normal (for a normal distribution)
  • Sine

Variables

The 4 variables are, m, k, b, and c change their meanings slightly depending on the curve type.

For Linear and Polynomial types, they represent what we are used to seeing in the y = mx + b formula:

  • m = slope (positive numbers for up, negative for down)
  • k = exponent (1 = linear)
  • b = y-intercept
  • c = x-intercept

For Logistic curves, they are:

  • m = slope of line in middle
  • k = Vertical size and direction of curve (positive numbers for up, negative for down)
  • b = moves line vertically from its starting point
  • c = moves line horizontally from its starting point

For Normal curves, they are:

  • m = width of the "bump" of the curve. Roughly equivalent to changing the standard deviation.
  • k = height of the "bump"
  • b = moves line vertically from its starting point
  • c = moves line horizontally from its starting point

Code

The data is held in the very simple ResponseCurve class but the calculations are performed in the Consideration class in Consideration::GetConsiderationValue.