Advanced Topics in Forest
Biometrics  FOR6934
A few notes on transformation in
regression
What is the impact of transforming
variables in regression?
±
When units of
x
changed
²
Regression coefficients are applied to the transformed
value of
x
²
No impact on tests, fit statistics
±
Units of
y
are changed
²
Predictions are in the transformed units
²
No impact on tests of significance
²
Fit statistics
are impacted substantially
±
Rsquared as automatically computed is the percentage of
variation in the
transformed variable
that is explained by the
x
variables
±
RMSE is in
transformed units
Æ
You must backtransform data to get accurate fit statistics
to properly compare equations!
What is backtransformation?
±
Predictions are transformed
back
into the
original units by using the inverse function
²
E.g., if you predict
√
height, change these predictions
into height by squaring them
±
Using the predictions
in original units,
compute
residuals
in original units
Æ
Then compute
SSres,
to get:
•
Std Err of Estimate = RMSE =
√
MSres
•
Rsquared (1 –
SSres/SSy
)
Example
DBH
HEIGHT
41.5
26.9
17.4
22.7
32.8
24
20.5
22.5
44.3
31.7
10.7
8
10.1
8
12.1
11
8.1
5.5
4.5
2.8
27.4
27.1
32.2
22
52.8
27.7
53.5
32.3
63.6
29.1
42.8
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 Spring '08
 Staff

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