title: Get uncertainties of predicted values after linear regression
body: <p>I perform a multiple linear regression:</p>
  <pre><code>dependent &lt;- c(1, 3, 2, 4, 6, 8)
  independent_a &lt;- c(1, 2, 3, 6, 5, 4)
  independent_b &lt;- c(0, 3, 2, 5, 9, 8)
  
  model &lt;- lm(dependent ~ independent_a + independent_b)
  summary(model)
  </code></pre>
  <p>The predicted data are shown upon <code>fitted(model)</code>. How can I get the uncertainty of these values?</p>
  <p>I am aware that I can calculate them applying error propagation from the uncertainties of the intercept and the coefficients that are shown with <code>summary(model)</code>. However, this calculation would assume uncorrelated contributions to the uncertainty whereas the multiple linear regression would suggest correlated contributions.</p>