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“Sale of umbrella may be positively correlated to traffic accidents in the urban area with rainfall” statement is a lurking variable. Demand for umbrella will go up and traffic accidents may increase due to roads being slippery and blurred vision.
Correlation between a higher consumption of tea and a low risk of a lung cancer may be attributed to the presence of a specific gene variant. If tea consumers have the gene, a risk of a lung cancer may be lower. However, if the gene is not present, the high tea consumption does not reduce the risk of a lung cancer.
People eating more organic food live longer. Confounding variable could be physical exercise in the sense that such people may be doing a lot of physical exercises, thus, keep fit and reduce the risk of diseases.
City mayor's salary is positively correlated with the average price of rum in the city. Positive correlation could be a result of such lurking variable as taxes. Expensive rum brings more taxes, which lead to higher incomes of the city. This chain brings us to the level of mayor's salary; high price – more taxes – higher incomes – higher salary, low price – less taxes – lower incomes – lower salary.
Years of schooling (IV) is positively correlated with the level of income (DV). Source of intervening variable could be industriousness. Industrious people learn for more years hence acquires more knowledge and are able to secure well paying jobs.
Level of income (IV) is positively correlated with the amount of money spent on clothes (DV). Winning a lottery could increase income level thus enable a person to spend a lot of money on clothes.
The amount of foreign aid received by a country (IV) is positively correlated with the quality of public service in the country (DV). Better international relations may lead to increased foreign aid thus have enough resources to improve the public service.
Assessment of human rights violations (IV) is negatively correlated with the amount of foreign aid received (DV). Corruption could be the intervening factor. In countries where human rights are violated, there is a high level of corruption. Therefore, these countries receive less foreign aid.