Page 132 - Statistics II for Dummies

116 Part II: Using Different Types of Regression to Make Predictions

Anticipating Nonlinear Regression

Nonlinear regression comes into play in situations where you have graphed
your data on a scatterplot (a two-dimensional graph showing the x variable on
the x-axis and the y variable on the y-axis; see the next section “Starting Out
with Scatterplots”), and you see a pattern emerging that looks like some type
of curve. Examples of data that follow a curve include changes in population
size over time, demand for a product as a function of supply, or the length
of time that a battery lasts. When a data set follows a curved pattern, the
time has come to move away from the linear regression models (covered in
Chapters 4 and 5) and move on to a nonlinear regression model.

Suppose a manager is considering the purchase of new office management
software but is hesitating. She wants to know how long it typically takes
someone to get up to speed using the software.
What’s the statistical question here? She wants a model that shows what the
learning curve looks like (on average). (A learning curve shows the decrease
in time to do a task with more and more practice.) In this scenario, you have
two variables: time to complete the task and trial number (for example, the
first try is designated by 1, the second try by 2, and so on). Both variables
are quantitative (numerical) and you want to find a connection between two
quantitative variables. At this point, you can start thinking regression.

A regression model produces a function (be it a line or otherwise) that
describes a pattern or relationship. The relationship here is task time versus
number of times the task is practiced. But what type of regression model do
you use? After all, you can see four types in this book: simple linear regres-
sion, multiple regression, nonlinear regression, and logistic regression. You
need more clues.

The word “curve” in learning curve is a clue that the relationship being mod-
eled here may not be linear. That word signals that you’re talking about a
nonlinear regression model. If you think about what a possible learning curve
may look like, you can imagine task time on the y-axis and the number of the
trial on the x-axis.
You may guess that the y-values will be high at first, because the first couple
of times you try a new task, it takes longer to perform. Then, as the task is
repeated, the task time decreases, but at some point more practice doesn’t
reduce task time much. So the relationship may be represented by some sort
of curve, like the one I simulate in Figure 7-1 (which can be fit by using an
exponential function).

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