Modeling with functions
Real data comes with no rule attached. How do you choose one, fit it, and know when to believe it?
Where you are 5 inside
What this area is about
A model is a function chosen to describe something real: a line, a quadratic, an exponential such as 40(1.15)^t. Modeling is the whole cycle around that choice. You decide which family fits, write the rule from data or words, say what each number in it means, and judge where its predictions can be trusted.
How these fit together
Building a model. Choosing a function family for data uses differences, ratios and the shape of a scatter plot to pick a family. Building a model from a description turns a written account into a rule with named quantities and units.
Reading a model. Interpreting the numbers in a model says what the starting value, the rate or the factor means in the situation.
Trusting a model. Where a model holds separates safe predictions inside the data from risky ones outside it. Judging and comparing models compares predictions with real values to choose between candidates.
A path through it
Choose a function family first. Then build a model from a description and interpret its numbers. After interpreting comes where a model holds, and judging a model’s fit last.
From here, fitting with technology hands the arithmetic of a best fit to a calculator or spreadsheet.