To decide, let's try to think of examples and counterexamples to the statement. First, we will draw a scatter lot that shows positive association where the relationship between variables is proportional.
Proportional Relationship
Imagine we are at an ice cream shop. Let x be the number of ice cream scoops we buy and y their total price.
Intuitively, the more scoops we buy, the more we will have to pay. This is why the association between the variables is positive. Now, here is a scatter plot showing the total cost for different numbers of scoops.
We know that these two variables are proportional because each new scoop costs the same. Also, the data points align to form a line.
Non-proportional Relationship
Now we want to come up with a positive association where the variables are not proportional. This means that both variables will be increasing at the same time but the graph of the data set will not be a line. Let's think of water lilies and how they grow.
If the conditions are right, the number of lily pads in a pond doubles each day. We can show this in a graph. Let x represent the days and y be the number of lilies in a pond.
The association between x and y is positive because the number of lilies grows as time passes. The relationship between x and y is not proportional because the data points do not form a line.
Summary
Let's take a look at the statement one more time.
A scatter plot that shows a positive association suggests that the relationship is proportional.
We found both an example and a counterexample to the statement. This is why the statement is sometimes true.
