Yes, that was regeneration.

There is no indication in Old Who or the New Series that regeneration is exclusively limited to being uncontrollably triggered by fatal events.

Although regeneration is usually seen in the show as an "emergency fail-safe" feature, we're also shown very explicitly that most Time Lords choose to regenerate for reasons other than imminent death. Romana is the most prominent example, although Borusa also comes to mind (the man seems to have gone through bodies like some people go through ties).

The Doctor just leads such a hard life that his regenerations come more violently than most Time Lords'.

The fact that it was forced on him by the Time Lords doesn't change anything either; the High Council has repeatedly been shown to have control over the regeneration technology (for example, offering the Master a new set of regenerations if he helped them in The Five Doctors). There's no reason to assume that the process they used to change the Second Doctor into the Third was not regeneration; in fact, their dialogue in that scene makes it clear that the process is identical to that which turned the First into the Second (though "regeneration" wasn't yet really a term being used by the show).

Was the Second Doctor's "regeneration" actually a regeneration?
I am trying to interpreting the output of nls(). I have read this post but I still don't understand how to choose the best fit. From my fits I have two outputs:

&gt; summary(m)

  Formula: y ~ I(a * x^b)

  Parameters:
  Estimate Std. Error t value Pr(&gt;|t|)    
  a 479.92903   62.96371   7.622 0.000618 ***
  b   0.27553    0.04534   6.077 0.001744 ** 
  ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

  Residual standard error: 120.1 on 5 degrees of freedom

  Number of iterations to convergence: 10 
  Achieved convergence tolerance: 6.315e-06 


and

&gt; summary(m1)

  Formula: y ~ I(a * log(x))

  Parameters:
  Estimate Std. Error t value Pr(&gt;|t|)    
  a   384.49      50.29   7.645 0.000261 ***
  ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

  Residual standard error: 297.4 on 6 degrees of freedom

  Number of iterations to convergence: 1 
  Achieved convergence tolerance: 1.280e-11


The first one has two parameters and smaller residual error. The second only one parameter but worst residual error. Which is the best fit?
