You can simply use the F test and anova to compare them. Here are some codes.    

&gt; x &lt;- 1:10
&gt; y &lt;- 2*x + 3                            
&gt; yeps &lt;- y + rnorm(length(y), sd = 0.01)
&gt; 
&gt; 
&gt; m1=nls(yeps ~ a + b*x, start = list(a = 0.12345, b = 0.54321))
&gt; summary(m1)

Formula: yeps ~ a + b * x

Parameters:
   Estimate Std. Error t value Pr(&gt;|t|)    
a 2.9965562  0.0052838   567.1   &lt;2e-16 ***
b 2.0016282  0.0008516  2350.6   &lt;2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.007735 on 8 degrees of freedom

Number of iterations to convergence: 2 
Achieved convergence tolerance: 3.386e-09 

&gt; 
&gt; 
&gt; m2=nls(yeps ~ a + b*x+c*I(x^5), start = list(a = 0.12345, b = 0.54321,c=10))
&gt; summary(m2)

Formula: yeps ~ a + b * x + c * I(x^5)

Parameters:
   Estimate Std. Error  t value Pr(&gt;|t|)    
a 3.003e+00  5.820e-03  516.010   &lt;2e-16 ***
b 1.999e+00  1.364e-03 1466.004   &lt;2e-16 ***
c 2.332e-07  1.236e-07    1.886    0.101    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.006733 on 7 degrees of freedom

Number of iterations to convergence: 2 
Achieved convergence tolerance: 1.300e-06 

&gt; 
&gt; anova(m1,m2)
Analysis of Variance Table

Model 1: yeps ~ a + b * x
Model 2: yeps ~ a + b * x + c * I(x^5)
  Res.Df Res.Sum Sq Df     Sum Sq F value Pr(&gt;F)
1      8 0.00047860                             
2      7 0.00031735  1 0.00016124  3.5567 0.1013
&gt;


How to read the the goodness of fit on nls of R?
Rashi (Sanhedrin 44b, s.v. D'ba'ya) relates the story of Shimon ben Shetach's capture of 80 witches. He instructed his students to pick up the witches because the sorcery would be powerless against the students if the witches were ungrounded. Is this to say that sorcery does not work unless the practitioner is grounded?

If so, how can we interpret the Midrash (Bamidbar Rabba, 20:20) that states that Bilaam used sorcery to fly through the air?
