3.2 Non-Linear Parameters - Quadratic - notes

# 3.2 Non-Linear Parameters - Quadratic - notes -...

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Objective [3.2] – Notes Part 1 – Quadratic Be familiar with and recognize the algebraic form(s) for all three models, including their corresponding parameters and if those parameters have any meaning in the context of the functional relationship (e.g. does a parameter control the initial value, rate of change (shape), decreasing or increasing (flip), max/min, limiting values, etc.) In a linear model both parameters (linear and constant) have meaning in the “real” business world. The linear parameter was the constant rate of change of a relationship and the constant parameter is the initial value. This will NOT be that case for other models. Some parameters may not have any “real” business meaning. Some will be derived from other values that do have meaning and yet some may just be “fitting” parameters with no specific meaning. So what about the parameters in the three models we have left to study, quadratic, exponential and logistic. Do their parameters all have business meanings? How do we find their parameter values given some information (data)? What is the minimum information (data) we need to find values for all of them? Quadratic Model Parameters There are two “forms” of the quadratic model( function). Recall the first is standard form and the second is vertex form. 2 2 2 2 2 () ( ) ( ) (2 ) ( ) note: 2 , D t at bt c D t a t r s at ar t s ar b ar c s ar     So do , , abc or ,, a r s have meaning? It turns out yes and no. Standard Form Parameter Interpretations 2 D t at bt c c is definitely still the initial value, just let the input 0 t in the standard form. Yet s is definitely NOT the initial value,

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3.2 Non-Linear Parameters - Quadratic - notes -...

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