Final answer:
A Pearson's r² of .36 means that 36% of the variation in city crime rates is explained by variation in median incomes, showing a moderate association between the two variables.
Step-by-step explanation:
If you calculated a Pearson's r² of .36 between median incomes and city crime rates, it means that 36% of the variance in city crime rates can be explained by the variance in median incomes, indicating there is a degree of association or relationship between these two variables. The coefficient of determination, r², is the square of the correlation coefficient which shows the proportion of variance shared between the two variables being measured. In this context, a Pearson's r² of .36 suggests a moderate relationship, meaning that as median income varies, there is a moderate tendency for city crime rates to vary correspondingly.
It should also be noted that the remaining 64% of the variance in city crime rates is not explained by median incomes and could be due to other factors or random variation. This is derived from the concept that the sum of r² and the unexplained variance should equal 1, or 100%.