title: Using : or . in lm() in R with all predictors typed out or with the dot (.) produces the same statistics?
body: <p>I have read ?lm and help(&quot;formula&quot;) in R but can't seem to grasp the following results.</p>
  <p>Why am I getting the same statistics with the following?</p>
  <p>(a) x1 + x2 + x1:x2</p>
  <p>(b) x1 + x2 + x1*x2</p>
  <p>I am getting the same statistics with the following as well.</p>
  <p>(c) . + x1:x2</p>
  <p>(d) . + x1*x2</p>
  <p>Now I know the reason that (a) &lt;&gt; (c) and (b) &lt;&gt; (d) is because . means all predictors and x1 * x2  means x1 + x2 + x1*x2, but why is it that (a) = (b) and (c) = (d)?</p>