title: Question on nls fit in R - why is this such a strange fit?
body: <p>I'm trying to perform a non linear fit to some simple data (corn yield by year).  It's straight forward enough to do it with lm in R, but some of the data would fit better if there was a curve allowed, something on the order of year^1.5 or so.</p>
  <pre><code>x &lt;- c(1979L, 1980L, 1981L, 1982L, 1983L, 1984L, 1985L, 1986L, 1987L, 
  1988L, 1989L, 1990L, 1991L, 1992L, 1993L, 1994L, 1995L, 1996L, 
  1997L, 1998L, 1999L, 2000L, 2001L, 2002L, 2003L, 2004L, 2005L, 
  2006L, 2007L, 2008L, 2009L, 2010L, 2011L, 2012L, 2013L, 2015L, 
  2016L, 2017L, 2018L, 2019L)
  
  y &lt;- c(47.3, 25.4, 39, 56.4, 41.4, 56.1, 60.3, 58, 64, 35, 56, 54, 
  37, 80, 59, 88, 55, 87, 90, 99, 93, 90.4, 80.7, 35, 80.2, 104.9, 
  59.9, 43.5, 97.9, 106, 132, 121.7, 120.1, 63.9, 142.5, 129.9, 
  114.8, 122.1, 164.3, 133.9)
  
  yield_model &lt;- nls(y ~ x^a,start=list(a = 1))
  
  plot(x,y)
  lines(x,predict(yield_model),lty=2,col=&quot;red&quot;,lwd=3)
  
  &gt; yield_model2
  Nonlinear regression model
   model: y ~ x^a
   data: parent.frame()
   a 
  0.5778 
  residual sum-of-squares: 46984
  
  Number of iterations to convergence: 8 
  Achieved convergence tolerance: 7.566e-09
  </code></pre>
  <p>Why does the nls fit so poorly (visible if you plot it)?  Did I do something wrong?  You can imagine that a slight curve in a fit to the data would be better, along with a trend.  It's like nls removed the trend or something.  Any help would be great.</p>