Is it okay to rely on the Residual Standard Error of a zero intercept linear regression (given that R-squared is not reliable in this case)? $y = f(x,...)$
$y$ represents the total effort in hours to complete a mix of tasks (each $x$ is a different mix) of varying complexity. It might be a non-linear relationship, but for now, I only have the count of tasks. No complexity data. I'd like to understand the correlation between total effort and task count.
A simple regression throws this up:
> summary(lm(data=dat, y ~ x))

Call:
lm(formula = y ~ x, data = dat)

Residuals:
     Min       1Q   Median       3Q      Max 
-2912.84  -189.26    12.88   148.09  3138.23 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)      -148.09     102.96  -1.438    0.155    
x                 146.76      13.89  10.568 1.69e-15 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 724.2 on 62 degrees of freedom
Multiple R-squared:  0.643, Adjusted R-squared:  0.6373 
F-statistic: 111.7 on 1 and 62 DF,  p-value: 1.687e-15


I re-ran it with a forced zero intercept.
It now says:
> summary(lm(data=dat, y ~ 0 + x))

Call:
lm(formula = y ~ 0 + x, data = dat)

Residuals:
    Min      1Q  Median      3Q     Max 
-2775.5  -287.4  -118.5     0.0  3389.7 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
x                 137.24      12.31   11.15   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 730.3 on 63 degrees of freedom
Multiple R-squared:  0.6635,    Adjusted R-squared:  0.6582 
F-statistic: 124.2 on 1 and 63 DF,  p-value: < 2.2e-16

Question: Which of the two above is a better fit? Should the Residual Standard Error* (RSE) be the guide? Or should I simply go with the second model because a zero-intercept makes sense in this case?
Note: The post shared by Nick Cox states that $R^2$ must not be relied upon for zero-intercept cases. I don't fully understand the math described there but I'm hoping that it is okay to rely on the Residual Standard Error in a zero-intercept scenario. Could someone please confirm this as well?
*Reference: This article says RSE is also a goodness-of-fit measure.

While this remains open (full disclosure: I voted to close) I will offer another answer, which is (to start negatively) that the question is hard and unclear, as it mixes together various general issues with distinctly limited specific details arising from the analysis of one dataset. I will also try to bring together various comments already made.
So far as I can see, nothing in the question really illuminates quite what is best or better as an analysis for the dataset being alluded to or for other datasets on the relation between (if I understand this correctly)
number of tasks completed as a predictor
and
total effort as an outcome.
In abstraction, it does seem that zero effort would imply zero achievement as a limiting condition, but that said

*

*The relevance of this as a constraint is an open question, but even if it seems compelling, it still allows many different functional forms, starting with $y = bx$, $y = bx + cx^2$, $y = ax^b$, and so on. Yet broader is a possibility that no simple algebraic specification will work well.


*To advise well on what to do with the data, we need to see the data, which is in principle easy for a small dataset. (I asked in comments for a scatter plot, but a listing would be even better.)
The characteristic terseness of lm output from R is defensible on various grounds but it is not sufficient to advise here on which model makes most sense (substantively, scientifically) and fits the data well, which in my view should be the main questions here.
The idea that a single summary criterion should be sought to make a decision for you seems utterly misguided here, and in general.
