title: Determine where line slope changes (algorithm)
body: <p>If you plot the numbers below, you get a "volatility smile": the 
  numbers follow one linear slope (the left slope), and then change to 
  following another linear slope (the right slope). </p>
  
  <p>I have several sets of data like this and want to know where the slope 
  changes. Notes: </p>
  
  <ul>
  <li><p>The slope change usually occurs between points </p></li>
  <li><p>I don't know how many points have the left slope and how many have 
  the right slope. </p></li>
  <li><p>There's no guarentee about the sign/magnitude of either slope or 
  the relation between the slopes. Each slope may be negative or 
  positive, and either might be greater than the other. </p></li>
  <li><p>If the slopes are identical, the program should report this as a 
  special case. </p></li>
  </ul>
  
  <pre>
  0.1613 
  0.1596 
  0.1579 
  0.1561 
  0.1544 
  0.1528 
  0.1511 
  0.1495 
  0.1478 
  0.1462 
  0.1446 
  0.1431 
  0.1415 
  0.1416 
  0.1418 
  0.1419 
  0.1421 
  0.1422 
  0.1424 
  0.1425 
  0.1426 
  0.1428 
  0.1429 
  0.1431 
  </pre>