title: lm() Regression with interactions for an entire dataframe
body: <p>I know there is a shortcut in <code>R</code>to run an <code>lm()</code>regression on all a dataframe like this : </p>
  
  <pre><code>reg&lt;-lm(y~.,data=df)
  </code></pre>
  
  <p>With df having explanatory variables x1, x2, ... x5, so it is the same as writing </p>
  
  <pre><code>reg&lt;-lm(y~x1+x2+x3+x4+x5,data=df)
  </code></pre>
  
  <p>But this doesn't include interactions terms like x1:x2, ... Is there a shortcut in <code>R</code>to run a regression on all columns of a dataframe with the interactions ?
  I am looking for 2 shortcuts which will have the same effects as </p>
  
  <pre><code>reg&lt;-lm(y~x1*x2,x1*x3,x1*x4,x1*x5,x2*x3,...)
  reg&lt;-lm(y~x1*x2*x3*x4*x5) # this one will have interactions between the 5 variables
  </code></pre>