Final answer:
The minimum absolute value of r required to prove causation between variables does not exist; any value of r, no matter how close to +/-1, can only indicate correlation, not causation.
Step-by-step explanation:
The question you've asked pertains to the value of the correlation coefficient, commonly denoted as r, and its role in proving causation between an explanatory variable and a response variable. It's important to clarify that no matter the value of r, be it perfect correlation at +/- 1.0, a strong correlation at +/- 0.80, or any other value, correlation on its own does not imply causation. The correct answer to the question is b) there is no such value; correlation never implies causation. Even with a coefficient of perfect correlation, we cannot conclusively prove causation without conducting a proper experiment or including additional statistical analysis to control for other variables.
The sign of r indicates the direction of the relationship; a positive correlation means that as one variable increases, the other tends to increase as well, while a negative correlation implies the opposite. The closer the value of r is to either -1 or +1, the stronger the linear relationship between the variables. However, this strength of correlation does not establish a cause-effect relationship.