A paper by Emily Oster of Harvard University, published in the Social Science Research Network's electronic library in 2004, explored the "possibility that the witchcraft trials [between 1520 and 1770] are a large-scale example of violence and scapegoating prompted by a deterioration in economic conditions. In this case, the downturn was brought on by a decrease in temperature and resulting food shortages. [. . .] Witches became target for blame because there was an existing cultural framework that both allowed their persecution and suggested that they could control the weather."28 Time series plots of standardized temperatures and standardized trials, both of which incorporated trends over all of Europe, show a rather convincing pattern: Many decades for which there was a relative trough in temperature showed an accompanying spike in trials; most notably, when temperatures reached an extreme low-point around 1740, trials hit an alltime high.
a. If we consider the relationship between witchcraft trials and weather, which should play the role of explanatory variable and which response?
b. Suppose that instead of looking at time series plots for both variables, we looked at a scatterplot for trials and temperature. Would the correlation be positive or negative?