title: How to check interaction effects for a lot of predictors in R
body: <p>I am trying to fit a regression model in R, after figuring out the main predictors, I want to check the interaction effects for the predictors. However, there are 14 predictors in total, which means hundreds of combinations possible.
  If I do this:</p>
  
  <pre><code>   lm.fit2=lm(medv~chas*dis*tax*black*rm*lstat*age*nox*zn*crim*rad*indus*ptratio,data=Boston)
  </code></pre>
  
  <p>summary(lm.fit2)
  Then error occurs because the degree of freedom reduces to negative which is not available. </p>
  
  <p>To make it work:</p>
  
  <pre><code>lm.fit2=lm(medv~chas*dis*tax*black*rm,data=Boston)
  summary(lm.fit2)
  </code></pre>
  
  <p>However, this still gives me too many options:</p>
  
  <pre><code>Coefficients:
                          Estimate Std. Error t value Pr(&gt;|t|)
  (Intercept)           -2.082e+02  1.798e+02  -1.158    0.248
  chas                  -2.585e+03  1.820e+03  -1.420    0.156
  dis                    2.545e+01  6.613e+01   0.385    0.701
  tax                    4.098e-01  3.021e-01   1.356    0.176
  black                  3.434e-01  4.622e-01   0.743    0.458
  rm                     4.234e+01  3.015e+01   1.405    0.161
  chas:dis               8.677e+02  6.350e+02   1.367    0.172
  chas:tax               6.656e+00  5.232e+00   1.272    0.204
  dis:tax               -7.457e-02  1.259e-01  -0.593    0.554
  chas:black             6.931e+00  4.936e+00   1.404    0.161
  dis:black             -6.838e-02  1.688e-01  -0.405    0.686
  tax:black             -7.198e-04  7.791e-04  -0.924    0.356
  chas:rm                3.295e+02  2.864e+02   1.150    0.251
  dis:rm                -5.586e+00  1.084e+01  -0.515    0.606
  tax:rm                -7.681e-02  5.049e-02  -1.521    0.129
  black:rm              -6.455e-02  7.744e-02  -0.833    0.405
  chas:dis:tax          -1.971e+00  2.520e+00  -0.782    0.435
  chas:dis:black        -2.280e+00  1.648e+00  -1.383    0.167
  chas:tax:black        -1.835e-02  1.370e-02  -1.339    0.181
  dis:tax:black          1.878e-04  3.227e-04   0.582    0.561
  chas:dis:rm           -9.001e+01  1.018e+02  -0.884    0.377
  chas:tax:rm           -8.002e-01  8.687e-01  -0.921    0.357
  dis:tax:rm             1.447e-02  2.063e-02   0.702    0.483
  chas:black:rm         -9.037e-01  7.670e-01  -1.178    0.239
  dis:black:rm           1.414e-02  2.765e-02   0.511    0.609
  tax:black:rm           1.318e-04  1.301e-04   1.013    0.312
  chas:dis:tax:black     5.364e-03  6.461e-03   0.830    0.407
  chas:dis:tax:rm        1.592e-01  4.289e-01   0.371    0.711
  chas:dis:black:rm      2.436e-01  2.619e-01   0.930    0.353
  chas:tax:black:rm      2.293e-03  2.250e-03   1.019    0.309
  dis:tax:black:rm      -3.452e-05  5.286e-05  -0.653    0.514
  chas:dis:tax:black:rm -4.712e-04  1.098e-03  -0.429    0.668
  </code></pre>
  
  <p>So if I include more predictors it is more likely taking much more time to make decisions. 
  I want to ask if there is any way I can check the interaction effects more quickly.</p>