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We have spent a lot of the semester analyzing functional models. That is, algebraic functions that describe the relationship between quantities in the real world. However, in the real world, we don′t usually have an algebraic function. Instead, we have a spreadsheet full of data.

The process of creating an algebraic function that approximates real world data is called Regression. The idea is to find a function that comes as close as possible to as many data points as possible.

Your project is to write a short paper (about 3 pages including graphs). It should take the form of a report to a boss or a client. Your paper should:

Describe a real-world relationship between quantities that you have data for. Be sure to reference the source of the data.

Give an algebraic functional model that approximates the data.

Use a graph to show a scatterplot of the data and the algebraic function.

Explain why you chose that particular type of algebraic function (linear, quadratic, etc.) and not the others. You should use the scatterplot and the features of the real-world situation to do this. You should also show the graphs of all of the other function types and explain why they are the wrong fit.

Calculate the following using the algebraic function and interpret what they mean for the real-world data:

The x- and y-intercepts (if any)

The slope/derivative

The concavity

Any relative extreme points or inflection points

Use your functional model to make a prediction about the data in the near future.