title: How to compute regression coefficients with proc mixed in sas?
body: <p>Here are <a href="http://www.megafileupload.com/eSdb/test.txt" rel="nofollow noreferrer">my data</a>. Data are structured like so: <code>id x1 x2 x3 y</code>.</p>
  
  <p>I used <code>proc mixed</code> to analyze it, but now want to determine regression coefficients and I don't know how to do it. I'm only a beginner with <code>sas</code>. From the results I see that <code>x1</code>, <code>x2</code>, <code>x3</code> and <code>x1x2x3</code> are the significant effects, but how to determine the coefficients <code>alpha, beta, gamma, delta, theta</code>:</p>
  
  <p><code>y = theta + alpha*x1  + beta*x2 + gamma*x3 + delta*x1*x2*x3</code></p>
  
  <p>This is my code:</p>
  
  <pre><code>ods graphics on;
  proc mixed data=test;
    class x1 x2 x3;
    model y = x1 | x2 | x3 / solution residual;
    random id;
  run;
  ods graphics off;
  </code></pre>
  
  <p>EDIT 1: Here is a part of the table <code>Solutions for Fixed Effects</code>:</p>
  
  <p><a href="https://i.stack.imgur.com/tsg4S.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/tsg4S.png" alt="Solutions for Fixed Effects"></a></p>
  
  <p>Since <code>x1</code> has two levels, there are two rows for it in the table. Do I get the effect of <code>x1</code> by summing these two values: <code>-109.07</code> for the first row and <code>0</code> for the second, or should I do something else? Note that this is <code>2^k</code> design. The effect of <code>x1</code> should be computed as half the difference between the average values for <code>y</code> when <code>x1</code> is high (20) and when it is low (10).</p>