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Interpretation of regression tree output

To: <s-news@lists.biostat.wustl.edu>
Subject: Interpretation of regression tree output
From: "Ryan Danby" <rdanby@ualberta.ca>
Date: Thu, 14 Sep 2006 15:26:55 -0600
Hi All;

I've used S-plus for Windows v.6 to derive a regression tree that I pruned
to 11 terminal nodes using cross validation. The dependent variable is
forest canopy cover (%), independent variables are a number of terrain
variables like elevation, slope, etc.

From the output I'm given (pasted below) I'm trying to determine how much
(what percent) of the total variance my tree actually explains. How do I
determine this?

Ryan Danby


 *** Tree Model ***

Regression tree:
snip.tree(tree = tree(formula = spru2 ~ curv.t + elev + geol + r.sum + rock
+ slp + twi, data = T1, na.action = na.exclude, mincut = 5, minsize = 10,
mindev = 0.01), nodes = c(7., 41., 11., 32., 17., 6., 33., 43.))
Variables actually used in tree construction:
[1] "elev"  "r.sum" "rock"  "slp"   "geol"
Number of terminal nodes:  11
Residual mean deviance:  309.6 = 441500 / 1426
Distribution of residuals:
     Min.  1st Qu.   Median     Mean  3rd Qu.     Max.
 -71.1300  -9.4300  -0.7222   0.0000   0.6263  70.0100
node), split, n, deviance, yval
      * denotes terminal node

 1) root 1437 915800.0 15.1500
   2) elev<1298.5 615 556300.0 31.0700
     4) r.sum<497.5 456 307200.0 24.6900
       8) rock<10.5 425 290700.0 26.2600
        16) elev<1234.5 338 240400.0 29.0200
          32) slp<9.5 208 137500.0 23.6300 *
          33) slp>9.5 130  87180.0 37.6500 *
        17) elev>1234.5 87  37800.0 15.5500 *
       9) rock>10.5 31    990.2  3.0940 *
     5) r.sum>497.5 159 177200.0 49.3900
      10) rock<0.5 134 138500.0 54.2200
        20) elev<1208.5 64  50890.0 65.7500
          40) slp<11.5 9   6010.0 32.8800 *
          41) slp>11.5 55  33560.0 71.1300 *
        21) elev>1208.5 70  71340.0 43.6700
          42) geol:2,5,8,9 22   6783.0 18.0900 *
          43) geol:1,3,7 48  43560.0 55.4000 *
      11) rock>0.5 25  18760.0 23.5100 *
   3) elev>1298.5 822  86630.0  3.2280
     6) elev<1372.5 189  56490.0 11.6200 *
     7) elev>1372.5 633  12860.0  0.7222 *



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