Decreased chi-squared when fitting to log scaled data? I have a set of datapoints (call them $x$ and $y$), and am attempting to discern whether $y$ scales linearly or exponentially with $x$. To do this, I plot both $y$ as a function of $x$, and $\log y$ as a function of $x$. I then fit both of them to a linear function. Below are the two resulting plots; the first is for $y$, and the second is for $\log y$


Both of these fits appear to work quite well, which I attribute to the relatively small change in $y$ as a function of $x$. However, the reduced chi-squared, given by the fit function in gnuplot, is $\sim 100$ for the first fit, and $\sim 0.01$ for the second fit. What is the reason for this large discrepancy? Is one truly a better fit than the other, and my eyes are just deceiving me? Or does something funny happen when I start trying to fit to logarithmically-scaled data?
EDIT: Data has been uploaded here, relevant columns are column 2 ($x$) and column 4 ($y$).
 A: Using R I obtain
Call:
lm(formula = y ~ x, data = df)

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 138.02137    7.32173   18.85   <2e-16 ***
x             1.08185    0.07096   15.25   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 10.15 on 34 degrees of freedom
Multiple R-squared:  0.8724,    Adjusted R-squared:  0.8686 
F-statistic: 232.4 on 1 and 34 DF,  p-value: < 2.2e-16

and for the log-scale
Call:
lm(formula = log(y) ~ x, data = df)

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 5.0512158  0.0305019  165.60   <2e-16 ***
x           0.0044846  0.0002956   15.17   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.04229 on 34 degrees of freedom
Multiple R-squared:  0.8713,    Adjusted R-squared:  0.8675 
F-statistic: 230.1 on 1 and 34 DF,  p-value: < 2.2e-16

The two fits are equally good, because they posses approx. the same adjusted $R^2$. 
If I use a goodness of fit test to check the quality of the fit, both fits result in the same p-value: 
Pearson's Chi-squared test

data:  log(df$y) and lm.out2$fitted.values
X-squared = 1260, df = 1225, p-value = 0.2376

However, I receive a warning, that the $\chi^2$ approximation might be incorrect. Thus, I rerun the $\chi^2$ test using simulations. This yields 
data:  df$y and lm.out1$fitted.values
X-squared = 1260, df = NA, p-value = 1

In conclusion I would say that the fit is equally good in both cases. 
