1b_more_reg - What is the impact of transforming variables...

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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 ± R-squared 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 back-transform data to get accurate fit statistics to properly compare equations! What is back-transformation? ± 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 R-squared (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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1b_more_reg - What is the impact of transforming variables...

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