title: Interpretation coefficient for summary interaction variables in lm()
body: <p>In R with multiple regression lm() function , I have 2 interrogations:</p>
  <ol>
  <li><p>I want all interactions between 3 variables A, B and C (brute force interactions search) : ( A and B) + (B and A) + (A and C) + (C and A) + (B and C) + (B and C). What's the syntax for all interactions?
  Do I write:</p>
  <pre><code>lm(Y~ A * B * C)
  </code></pre>
  <p>Or</p>
  <pre><code>lm(Y~ (A + B + C) * (A + B + C))
  </code></pre>
  <p>?</p>
  </li>
  <li><p>I don't understand how build the final regression equation with coefficient associated to interactioned variables.
  For example for this output for summary:</p>
  </li>
  </ol>
  <p>Please consider this summary for interactions variables with lm</p>
  <pre><code>#(Intercept) 0.97849 0.02865 34.15 &lt;2e-16 *** 
  #f1High 3.00306 0.04052 74.11 &lt;2e-16 *** 
  #f2B -1.97878 0.04052 -48.83 &lt;2e-16 *** 
  #f1High:f2B 0.98924 0.05731 17.26 &lt;2e-16 *** 
  </code></pre>
  <p>Is the final equation will be?
  Y = 0.97 + 3 * f1High -1.97 f2B -1.97 * f2B + 0.98 * f1High * f2B ? – Theo75 24 mins ago</p>
  <p>Thanks a lot.
  Théo.</p>