Example of Random Forests® Regression

Note

This command is available with the Predictive Analytics Module. Click here for more information about how to activate the module.

A team of researchers collects data from the sale of individual residential properties in Ames, Iowa. The researchers want to identify the variables that affect the sale price. Variables include the lot size and various features of the residential property.

After initial exploration with CART® Regression to identify the important predictors, the team uses Random Forests® Regression to create a more intensive model from the same data set. The team compares the model summary table and the R2 plot from the results to evaluate which model provides a better prediction outcome.

These data were adapted based on a public data set containing information on Ames housing data. Original data from DeCock, Truman State University.

  1. Open the sample data set AmesHousing.mtw.
  2. Choose Predictive Analytics Module > Random Forests® Regression.
  3. In Response, enter Sale Price.
  4. In Continuous predictors, enter Lot FrontageYear Sold.
  5. In Categorical predictors, enter TypeSale Condition.
  6. Click Options.
  7. Under Number of predictors for node splitting, choose K percent of the total number of predictors; K = and enter 30. The researchers want to use more than the default number of predictors for this analysis.
  8. Click OK in each dialog box.

Interpret the results

For this analysis, the number of observations is 2930. Each of the 300 bootstrap samples randomly selects 2930 observations, with replacement, to create a tree. The method also uses 30% of the total number of predictors to split nodes. Also, the Response Information table shows common descriptive statistics for the observations.

Random Forests® Regression: Sale Price vs Lot Frontage, Lot Area, ...

Method Model validation Validation with out-of-bag data Number of bootstrap samples 300 Sample size Same as training data size of 2930 Number of predictors selected for node splitting 30% of the total number of predictors = 23 Minimum internal node size 5 Rows used 2930
Response Information Mean StDev Minimum Q1 Median Q3 Maximum 180796 79886.7 12789 129500 160000 213500 755000

The R-squared vs Number of Trees Plot shows the entire curve over the number of trees grown. The R2 value rapidly increases as the number of trees increases then flattens at approximately 91%.

Random Forests® Regression: Sale Price vs Lot Frontage, Lot Area, ...

Model Summary Total predictors 77 Important predictors 68 Statistics Out-of-Bag R-squared 90.90% Root mean squared error (RMSE) 24097.3281 Mean squared error (MSE) 580681222.4890 Mean absolute deviation (MAD) 14746.8323 Mean absolute percent error (MAPE) 0.0895

The Model summary table shows that the R2 values are slightly improved over the R2 values of the corresponding CART® analysis.

The Relative Variable Importance graph plots the predictors in order of their effect on model improvement when splits are made on a predictor over the sequence of trees. The most important predictor variable for predicting the sale price is Quality. If the importance of the top predictor variable, Quality, is 100%, then the next important variable, Living Area SF, has a contribution of 88.8%. This means that the square footage of the living is 88.8% as important as the overall quality of the property. The next most important variable is Neighborhood which has a contribution of 52.6%.

The scatterplot of fitted sale price versus actual sale price shows the relationship between the fitted and actual values for the OOB data. You can hover over the points on the graph to see the plotted values more easily. In this example, many points fall approximately near the reference line of y=x, but several points may need investigation to see discrepancies between fitted and actual values.

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