Mr. Trump has his share of support from the affluent and the well educated, but in the places where support for Mr. Trump runs the strongest, the proportion of the white population that didn’t finish high school is relatively high. So is the proportion of working-age adults who neither have a job nor are looking for one. The third-strongest correlation among hundreds of variables tested: the preponderance of mobile homes.

Trump counties include places that have voted for both Republicans and Democrats, and the strongest predictors of Trump support include how a county responded to two very different third-party candidates: Trump territory showed stronger support for the segregationist George Wallace in the 1968 election than the rest of the country, and substantially weaker support for the centrist former Republican John B. Anderson in 1980.

Mr. Trump has performed well thus far in Appalachian coal counties and in rural parts of Alabama and Mississippi, which are coping with economic and social dysfunctions like high unemployment rates and heroin addiction. But the Times analysis also shows the common thread between those places and more urban locations where Mr. Trump has either done well or is projected to.

In Revere, Mass., a working-class suburb of Boston, Mr. Trump won 73 percent of the Republican primary vote.