The statement which best describes the association between the variables X and Y is the <em>moderate positive association</em>. It is observable that the values of X and Y are increasing, however, not in a perfect manner as there are some minor deviations. But nonetheless, the direction is clear and the values are close to each other so they have a moderate positive association.
The derivative function gives the derivative of a function at each point in the domain of the original function for which the derivative is defined. We can formally define a derivative function as follows.
Definition:
let f be a function. The derivative function, denoted by f', is the function whose domain consists of those values of x such that the following limit exists:
Yes but to understand the answer, we need to dig into the mechanics of correlation. Correlation is a mathematical relationship between the change in two variables. For causation to occur without correlation, we must therefore lack that mathematical relationship.