Response Curve

Concept

Different types of response curves

A Response Curve is a mathematical formula that converts an input value into an output value.

Components

The Response Curve is comprised of a curve type and 4 variables. By changing these values, we change the "shape" of the curve and, therefore, how it converts the raw number into a meaningful value for our utility.

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.