Which of these pairs of variables would you expect to
be represented by a scatterplot with a positive correlation?
A. a person's height and the person's grade on the math
test
B. the depth of the water in a pond and the amount of
rainfall
C. the number of miles driven and the number of people
on the bus
D. the number of concert tickets purchased and the
number of concert tickets still available for purchase
A. a person's height and the person's grade on the math test
The pair of variables that you would expect to be represented by a scatterplot with a positive correlation is A. a person's height and the person's grade on the math test.
To determine which of these pairs of variables would be represented by a scatterplot with a positive correlation, we need to understand what a positive correlation means.
In a scatterplot, a positive correlation exists when an increase in one variable is associated with an increase in the other variable. In other words, as one variable increases, the other variable also tends to increase.
Let's analyze each option and determine whether they would exhibit a positive correlation:
A. A person's height and their grade on a math test:
It is unlikely that a person's height would have a strong influence on their performance in a math test. Therefore, there is no clear relationship between these variables, and they would not be expected to have a positive correlation.
B. The depth of the water in a pond and the amount of rainfall:
When it rains, the water level in a pond tends to increase; hence, there is a positive relationship between the depth of water and the amount of rainfall. This pair of variables would have a positive correlation.
C. The number of miles driven and the number of people on the bus:
As the number of miles driven increases, it is likely that more people will board the bus, leading to an increase in the number of people on the bus. Therefore, there is a positive relationship between these variables, and they would be expected to have a positive correlation.
D. The number of concert tickets purchased and the number of concert tickets still available for purchase:
Here, there is an inverse relationship between the number of concert tickets purchased and the number of tickets still available for purchase. As more tickets are purchased, the availability of tickets decreases. Therefore, these variables would not have a positive correlation.
In conclusion, the pairs of variables that would be expected to have a positive correlation are:
B. the depth of the water in a pond and the amount of rainfall
C. the number of miles driven and the number of people on the bus