Page 138 - Statistics II for Dummies

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

Searching for the best polynomial model

When fitting a polynomial regression model to your data, you always start
with a scatterplot so you can look for patterns; the scatterplot will give you
some idea of the type of model that may work. Always start with the simplest
model possible and work your way up as needed. Don’t plunge in with a high-
order polynomial regression model right off the bat. Here are a couple of rea-
sons why:
✓ High-order polynomials are hard to interpret, and their models are
complex. For example, with a straight line, you can interpret the values
of the y-intercept and slope easily, but interpreting a tenth-degree poly-
nomial is difficult (and that’s putting it mildly).

✓ High-order polynomials tend to cause overfitting. If you’re fitting the
model as close as you can to every single point in a data set, your model
may not hold for a new data set, meaning that your estimates for y could
be way off.

To fit a polynomial to a data set in Minitab, go to Stat>Regression>Fitted Line
Plot> and click on the type of regression model you want: linear, quadratic, or
cubic. (It doesn’t go beyond a third-degree polynomial, but these options
should cover 90 percent of the cases where a polynomial is appropriate.) Click
on the y variable from the left-hand box, and click Select; this variable will
appear in the Response (y) box. Click on the x variable from the left-hand box,
and click Select; it will appear in the Predictor (x) box. Click OK.
Following are steps that you can use to see if a polynomial fits your data.
(Statistical software can jump in and fit the models for you after you tell it
which ones to fit.)

1. Make a scatterplot of your data, and look for any patterns, such as a
straight line or a curve.
2. If the data resemble a straight line, try to fit a first-degree polynomial
(straight line) to the data first: y = b + b x.
0 1
If the scatterplot doesn’t show a linear pattern, or if the correlation isn’t
close to +1 or –1, move to step three.
3. If the data resemble the shape of a parabola, try to fit a second-degree
2
polynomial: y = b + b x + b x .
0 1 2
If the data fit the model well, stop here and refer to the later section
“Assessing the fit of a polynomial model.” If the model still doesn’t fit
well, move to step four.

12_466469-ch07.indd 122 7/24/09 9:39:08 AM