# Interpretation of logged regression

I have run a linear regression with the following equation (in r):

lm(formula = logTotal ~ Continent + logArea + Method + Servs)


where Total is $/ha/year (numeric), Area is hectare (numeric), Continent and Method are factors and Servs is numeric. It returns the output: Call: lm(formula = logTotal ~ Continent + logArea + Method + Servs) Residuals: Min 1Q Median 3Q Max -0.99416 -0.26931 -0.00622 0.28885 1.19875 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -1.82886 0.71446 -2.560 0.016903 * ContinentAsia 3.82452 0.60471 6.325 1.28e-06 *** ContinentAustralasia 4.52516 0.96517 4.688 8.35e-05 *** ContinentEurope 2.18022 0.48260 4.518 0.000130 *** ContinentGlobal 2.44750 0.74092 3.303 0.002881 ** ContinentNorth America 2.35244 0.55281 4.255 0.000256 *** ContinentSouth America 3.67853 0.61454 5.986 2.99e-06 *** logArea 0.03643 0.03583 1.017 0.318911 MethodCVM -0.18171 0.43296 -0.420 0.678300 MethodOther hedonic -1.53284 0.79781 -1.921 0.066165 . MethodValue Transfer 0.98101 0.29773 3.295 0.002941 ** Servs 0.10723 0.04273 2.509 0.018948 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.552 on 25 degrees of freedom (65 observations deleted due to missingness) Multiple R-squared: 0.7582, Adjusted R-squared: 0.6518 F-statistic: 7.127 on 11 and 25 DF, p-value: 2.501e-05  I wish to predict Total based on various inputs, however I'm a bit lost on fully understanding the output. If I wished to predict "Total" on the basis of: Continent:Global, Area:1 hectare, Method:CVM, Servs:11  is the following equation correct? exp(Total) = 2.44750 + exp(1*0.03643) - 0.18171 + (11*0.10723)  I have read UCLA's statistics help site's FAQ on log transformed regression. I feel like I've oversimplified it but I just keep reading that link over and over and still not fully understanding. Also read How to interpret logarithmically transformed coefficients in linear regression?. ## 1 Answer is the following equation correct? exp(Total) = 2.44750 + exp(1*0.03643) - 0.18171 + (11*0.10723) No, but close. Assuming you used natural log:$\ln{Total} = -1.82886+2.44750+\ln(1)\times0.03643-0.18171+11\times0.10723$Then, exponent on both sides:$Total = exp^{-1.82886+2.44750+\ln(1)\times0.03643-0.18171+11\times0.10723}$If your goal is just to predict, the above simple substitution will work fine. The$exp^{\beta}\$ think you read about online is pertinent when you wish to interpret the coefficient individually.

And here provides some resource on dealing with retransformation bias, which I didn't know until Dimitriy pointed that out.

• What about retransformation bias? Commented Oct 17, 2014 at 16:37
• @DimitriyV.Masterov Oh, that's handy! Thanks for the tips. Commented Oct 17, 2014 at 16:44