title: Inconsistency in scipy.odr output for different fit types?
body: <p>For <code>odr.set_job(fit_type=2)</code> (ordinary least squares) <code>odr.set_job(fit_type=0)</code> (explicit ODR) the uncertainties <code>sd_beta</code> and the covariance matrix <code>cov_beta</code> are significantly different for the two fit types for the same data - which has an error in the y-part, only.</p>
  <p>Has anyone an idea where this originates from?
  Below is a a code example for reproducing the effect.
  On the side: For the <em>hidden</em> scaling factor between <code>sd_beta</code> and <code>cov_beta</code> I found some help here: <a href="https://stackoverflow.com/questions/41028846/how-to-compute-standard-error-from-odr-results">How to compute standard error from ODR results?</a></p>
  <pre><code>import numpy as np
  import scipy.odr as spodr
  
  def linear_func(pars, x):
      &quot;&quot;&quot;Define a (linear) function to fit the data with.&quot;&quot;&quot;
      a, b = pars
      return b * x + a
  
  x = np.asfarray( [1.01585124, 2.03965699, 2.89148684] )
  y = np.asfarray( [1.16201599, 2.15275179, 2.87248892] )
  dy = np.asfarray( [0.15520856, 0.33160654, 0.45461028] )
  
  real_data = spodr.RealData(x, y, sy=dy)
  linear_model = spodr.Model(linear_func)
  odr = spodr.ODR(real_data, linear_model, beta0=[0., 1.])
  # fit_type=2 means least square fit
  odr.set_job(fit_type=2)
  out = odr.run()
  print('fit_type=2 -------------------------------------------')
  out.pprint()
  print('\n')
  
  # fit_type=0 means explicit ODR
  odr.set_job(fit_type=0)
  out = odr.run()
  print('fit_type=0 -------------------------------------------')
  out.pprint()
  </code></pre>
  <p>giving out the following result:</p>
  <pre><code>fit_type=2 -------------------------------------------
  Beta: [0.22131257 0.92950773]
  Beta Std Error: [0.0444006 0.03004  ]
  Beta Covariance: [[ 0.10678885 -0.06586652]
   [-0.06586652  0.04888189]]
  Residual Variance: 0.01846085213372428
  Inverse Condition #: 0.02685695006039764
  Reason(s) for Halting:
    Sum of squares convergence
  
  
  fit_type=0 -------------------------------------------
  Beta: [0.24510628 0.91688192]
  Beta Std Error: [0.07210707 0.03482789]
  Beta Covariance: [[ 2.29687687 -1.03022278]
   [-1.03022278  0.53584146]]
  Residual Variance: 0.0022636956774060857
  Inverse Condition #: 0.017439127336256896
  Reason(s) for Halting:
    Sum of squares convergence
  </code></pre>