Aims. We study the chemical origin of a set of complex organic molecules thought to be produced by grain surface chemistry in high mass young stellar objects (YSOs). Methods. A partial submillimeter line-survey was performed toward 7 high-mass YSOs aimed at detecting H₂CO, CH₃OH, CH₂CO, CH₃CHO, C₂H₅OH, HCOOH, HNCO and NH₂CHO. In addition, lines of CH₃CN, C ₂H₅CN, CH₃CCH, HCOOCH₃, and CH ₃OCH₃ were observed. Rotation temperatures and beam-averaged column densities are determined. To correct for beam dilution and determine abundances for hot gas, the radius and H₂ column densities of gas at temperatures >100 K are computed using 850 μm dust continuum data and source luminosity. Results. Based on their rotation diagrams, molecules can be classified as either cold (<100 K) or hot (>100 K). This implies that complex organics are present in at least two distinct regions. Furthermore, the abundances of the hot oxygen-bearing species are correlated, as are those of HNCO and NH₂CHO. This is suggestive of chemical relationships within, but not between, those two groups of molecules. Conclusions. The most likely explanation for the observed correlations of the various hot molecules is that they are "first generation" species that originate from solid-state chemistry. This includes H₂CO, CH₃OH, C ₂H₅OH, HCOOCH₃, CH₃OCH₃, HNCO, NH₂CHO, and possibly CH₃CN, and C₂H ₅CN. The correlations between sources implies very similar conditions during their formation or very similar doses of energetic processing. Cold species such as CH₂CO, CH₃CHO, and HCOOH, some of which are seen as ices along the same lines of sight, are probably formed in the solid state as well, but appear to be destroyed at higher temperatures. A low level of non-thermal desorption by cosmic rays can explain their low rotation temperatures and relatively low abundances in the gas phase compared to the solid state. The CH₃CCH abundances can be fully explained by low temperature gas phase chemistry. No cold N-containing molecules are found.