Final answer:
A positive correlation exists when two variables move in the same direction, and a negative correlation exists when two variables move in opposite directions. The correlation coefficient 'r' quantifies the strength and direction of the relationship, and correct answer choice is a) Positive correlation; negative correlation.
Step-by-step explanation:
The correct answer to the student's question is a) Positive correlation; negative correlation.
A positive correlation is a relationship in which the two variables move in the same direction. This means that as one variable increases, the other variable also tends to increase, and when one variable decreases, the other variable tends to decrease as well. This relationship is often represented by a scatter plot where the data points form a pattern that extends from the lower left to the upper right, indicating that the variables increase together.
Conversely, a negative correlation is a relationship where the variables move in opposite directions. In this case, when one variable increases, the other variable tends to decrease, and vice versa. Scatter plots of negatively correlated variables show a pattern that extends from the upper left to the lower right, demonstrating an inverse relationship between the variables.
The correlation coefficient, often denoted by r, quantifies the strength and direction of this relationship, ranging from -1 (perfect negative correlation) to +1 (perfect positive correlation), with 0 indicating no correlation between the variables. It's important to understand that correlation does not imply causation; it simply measures the degree to which two variables are associated with one another.