Question

the table, choose the relationship that best describes each set of variables.
variables | relationship
cost of running shoes and running speed | correlation, but no causation | correlation and causation
number of miles driven and the amount of gasoline used | correlation, but no causation | correlation and causation

Explanation:

For "cost of running shoes and running speed":

The cost of running shoes doesn't directly cause a change in running speed. A more expensive shoe might not necessarily make a person run faster (and vice versa), but there could be a weak correlation (e.g., higher - end shoes might be associated with better - trained runners who are faster, but the cost itself isn't the cause of speed). So the relationship is "correlation, but no causation".

For "number of miles driven and the amount of gasoline used":

As the number of miles driven increases, the amount of gasoline used also increases because driving more miles requires more gasoline (the number of miles driven causes the amount of gasoline used to change). And there is a correlation (a linear relationship, generally) between the two. So the relationship is "correlation and causation".

Answer:

• cost of running shoes and running speed: correlation, but no causation
• number of miles driven and the amount of gasoline used: correlation and causation