Interpretation of logged regression

Question

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?.

Answer 1

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:

$Total = exp^{-1.82886+2.44750+\ln(1)\times0.03643-0.18171+11\times0.10723}$

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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.