# [R] linear regression, log-transformation and plotting

Wed Sep 7 12:17:58 CEST 2011

```Hello,

I've some questions concerning log-transformations and plotting of the regression lines. So far as I know is it a problem to log-transform values smaller than 1 (0-1). In my statistics lecture I was told to do a log(x+1) transformation in such cases. So I provide here a small example to explain my questions:

# Some example data for testing
a1 <-c(0.2,1.9,0.1,0.2,0.8,22,111.3,19.9,23.9,138,42.3,54.2,0.9)
b1 <-c(1.8,28.2,0.3,12.4,3.2,81.1,122.1,2.9,37.2,98.9,21,28.7,1.8)
data1  <- data.frame(a1,b1)

model <- lm(log(a1+1)~log(b1+1))

because of values less then one I did the log(x+1) transformation for running the lm. Is that correct so far? (Just to mention: These are example data so I haven't checked if the need a transformation at all)

Then some questions arise when it comes to plot the data. As usual I'd like to plot the original data (not log transformed) but in a log-scale.

I tried two approaches the standard plot function and ggplot.

# Plot with ggplot
ggplot()+
geom_point(aes(b1,a1,data=data1))+
geom_abline(aes(intercept=coef(model)[1],slope=coef(model)[2]))+
scale_y_log()+
scale_x_log()

# Plot with standard plot
plot(b1,a1,log="xy")
abline(model,untf=T)
abline(model,untf=F)

1) The regression lines are different for plot vs. ggplot(transformed or untransformed). So what is actually the correct line?

2) The regression line was calculated on basis of log(x+1), but the log scale on my axis is just simple log (without +1). So how are such cases usually treated? I thought about subtracting the value 1 from the intercept?

So my simple question: What is the best way to display such data with a regression line?

Thank you
/Johannes
--

```