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.

Answer from my comments
For a model without an intercept, if you want an r-squared-like measure of fit, you might use a version of Efron's pseudo r-squared. It's defined here:

*

*stats.oarc.ucla.edu/other/mult-pkg/faq/general/faq-what-are-pseudo-r-squareds/
With the caveat, that I wrote the former, there's an implementation in R in the rcompanion package, and in the performance package.
As an example:
A = c(1,2,3,4,5,6,7,8,9)
B = c(2,4,5,3,6,5,7,9,8)

model = lm(B ~ 0 + A)

summary(model)

    ### summary() reports an r-squared of 0.955.
    ###  This is probably not a desirable statistic to use
    ###   for a linear model without an intercept.

library(rcompanion)

accuracy(list(model))

   ### Efron.r.squared
   ###            0.67

library(performance)

r2_efron(model) 

   ### 0.6704986

For an OLS model with an intercept, this Efron's pseudo r-squared will be  equal to r-squared.
