I have a simple linear regression model, and I have done transformations on the response and the explanatory variable (see call in code below), and I obtained an r-squared of 0.415. When I back-transformed the response variable back to its original units, I get an r-squared of 0.29. My questions are two fold:
- First, why is there such a difference in the r-squared values when the same dataset is used;
- Second, if I report the root mean squared error for the second model (which I have read is the most appropriate action), can I still report the r-squared from the first model (i.e. r-squared of 0.42)?
Please see the two summary reports below. Thank you.
1. Call:
lm(formula = sqrt(Clay_Tot) ~ Dose, data = PedonsTx.11.LatLong)
Residuals:
Min 1Q Median 3Q Max
-3.9745 -0.6534 -0.1394 0.4876 4.5746
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.203414 0.248964 4.834 2.42e-06 ***
Dose 0.075897 0.005848 12.977 < 2e-16 ***
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.161 on 235 degrees of freedom
Multiple R-squared: 0.4175, Adjusted R-squared: 0.415
F-statistic: 168.4 on 1 and 235 DF, p-value: < 2.2e-16
2. Call:
lm(formula = Clay_Tot ~ Back.Dose.11, data = PedonsTx.11.LatLong)
Residuals:
Min 1Q Median 3Q Max
-22.316 -6.372 -2.337 2.649 60.211
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 7.8260736 1.4977945 5.225 3.84e-07 ***
Back.Dose.11 0.0070682 0.0007112 9.939 < 2e-16 ***
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 11.75 on 235 degrees of freedom
Multiple R-squared: 0.2959, Adjusted R-squared: 0.2929
F-statistic: 98.78 on 1 and 235 DF, p-value: < 2.2e-16