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12 Pages

### 8.2

Course: CS 102, Fall 2009
School: Charleston Law
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Word Count: 338

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8: Chapter Data-Driven Models 8.2 Function Tutorial Background: Data-Driven Models So far we've been given a model (dP/dt = kP) and used it to generate data. Research often requires us to build a model based on (limited) data. To do this, it helps to be familiar with the standard mathematical functions used for building models. Linear Functions Straight line is the simplest model Human beings are biased...

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8: Chapter Data-Driven Models 8.2 Function Tutorial Background: Data-Driven Models So far we've been given a model (dP/dt = kP) and used it to generate data. Research often requires us to build a model based on (limited) data. To do this, it helps to be familiar with the standard mathematical functions used for building models. Linear Functions Straight line is the simplest model Human beings are biased toward viewing patterns as straight lines with positive slope (Busemeyer et al. 1997) Linear Functions y = mx + b y b x x y y -y y 2 1 m= = x -x x 2 1 m: slope b: intercept Quadratic Functions f x= x+x a () a a + 2 1 0 2 y x a special case of ... Polynomial Functions f x a + x ++x a () n a =x . a+ . 1 0 . n n - 1 n - 1 f(x ax )= i f(x) i=0 n i x N: degree Square Root Function Useful when n - 1 f x a +-quantities a+ () n ax ++x =x a n . are 0 . 1 . 1 already squared: e.g. distance between two points (x1,y1 ) and (x2,y2 ) = n f(x) x (1 x 2+ 1 y 2 x 2 ( -2 -) y ) Exponential Function f x a + x ++x a () n a =x . a+ . 1 0 . n n - 1 n - 1 P) Pa ( =0 t k r t P(t) t Logarithmic Function Useful when n - 1 f x a +-dealing. a+ () n ax ++x a =x n .with . 1 0 1 inherently exponential measures, e.g. Richter scale for earthquakes. x n y Log/Log Plot for Power Laws f x a + x ++x a () n a =x . a+ . 1 0 . n n - 1 n - 1 Logistic Function f ...

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