Databases Reference
In-Depth Information
With your ANN model, R
2
should have soared to about 0.98. Why the
improvement?
View a scatter plot of xyRegress.csv.
Select X for the X axis, Y for the Y axis, and XNominal for the category.
This is a manufactured dataset to make a point about interaction effects.
You should recognize in the scatter plot that the relationship between X and Y
is very different
for
the XNominal
¼
“Y” observations as compared to
the XNominal
“N” observations. Additive modelers such as linear and
polynomial regression cannot detect the interaction, whereas the ANN has
no trouble doing so. This is its primary advantage. Obviously, you are very
unlikely to see such a dramatic effect in a real world dataset. Yet it does exist in
many datasets and your modeler needs to be able to detect that interaction.
¼
Top-Down Attribute Selection
The homes dataset contains all attributes previously determined to be
candidates for inclusion in the regression models: price, bathrooms, bedrooms,
cul-de-sac, den, diningRoom, latitude, laundry, longitude, lot, propertyType,
schoolDistrict, sqFeet, and yrBuilt.
Build linear, second- and third-order polynomial regression models for this
dataset.
View the regression summaries of each.
Using all available legitimate attributes, the linear model generates R
2
of
0.622 and the polynomial models generate 0.664 and 0.672 respectively. This
gives us a target to try to exceed when building an ANN model.
Using the same dataset, interactively build an ANN regression model. You
will find that it peaks out with an R
2
near 0.79.
Why is the performance of the ANN model better than the other two models?
One answer is that anANNpotentially fits the data better and a primary reason for
fitting the data is that the ANN can detect and model interaction between inputs
whereas the linear and polynomial models do not. By interaction, we mean that
the contributions of one input attribute vary depending on the value of a second
input attribute. The linear and polynomial models are additive. The level of one
input attribute in noway affects the contribution of a second input attribute. Yet in
the real world, there are frequent interactions between inputs. For example,
would you expect the value of a third bathroom in a one-bedroom home to be the
