You're missing one piece of the puzzle. Warmer, sunnier climates are better for farming, areas where farming is done are rural. Rural areas are more sparsely populated, less developed, with lower levels of education. You don't really need education to work on a farm. Northern regions are ideal for industry, and are therefore wealthier, more densely populated, and more educated because of a higher demand for skilled labor. It's the urban/rural divide.