Final answer:
A positive correlation indicates that two variables increase or decrease together, represented by a correlation coefficient near +1. A strong correlation does not imply causation, as illustrated by the example of microwave sales correlated with another unrelated variable. Confounding variables, like temperature in the ice cream and crime rate example, can explain correlations without direct causation.
Step-by-step explanation:
A positive correlation between two variables means that as one variable increases, so does the other, and when one decreases, the other does as well. This relationship is represented by a correlation coefficient, r, which ranges from -1 to +1. A coefficient close to +1 indicates a strong positive correlation. For example, there is a positive correlation between a person's height and weight. However, a strong correlation does not imply causation. An example given in class of a strong, but ultimately meaningless, correlation involved the number of microwaves sold and a completely unrelated variable, illustrating that not all correlations imply a direct or meaningful relationship.
The importance of distinguishing correlation from causation is highlighted by the example of ice cream sales and crime rates increasing during warmer months. A confounding variable, such as temperature, may explain the relationship, despite there being no direct causal link between ice cream sales and crime rates.