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I am presented with a linear regression result that yields the following coefficients:

Coefficients:
                                       Estimate Std. Error t value Pr(>|t|)    
(Intercept)                            0.627502   0.010139  27.782  < 2e-16 ***
A_num                                  0.047047   0.004919   9.703  3.7e-16 ***
Bhigh                                 -0.015863   0.004608  -3.510 0.000668 ***
Cin                                   -0.018517   0.003504  -2.801 0.006095 ** 

Where B has levels of (high, low) and C has levels of (in,out). This would, in my understanding provide four different intercepts one for each of the following

  • high, in
  • high, out
  • low, in
  • low, out

However, I do not happen to have any observations regarding one of them, say (high, in). I know that such observations must exist, but the sample does not include any such observation.

Would it still be valide to extend the interpretation to the unobserved scenario?

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Following offline discussion I have reached the conclusion that it is best to not making any claims regarding results that do not show up in the sample. This holds even if it is known for a fact that the scenarios do exists. The reason being, were the unobserved data points included in the sample the results may actually have turned out to be different. The difference may result from a variety of sources including different error and effect sizes, distribution, etc.

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