Bivariate Data Relations

Student: What relationships can there be between two different variables in bivariate data?

Mentor: Well, there can be positive relationships, negative (or inverse) relationships and then there are variables that have no relationship with one another. A positive relationship would exist if as one variable increases, the other variable increases or, if as one variable decreases, the other variable decreases.

Student: I'm not quite sure I understand how both of those situations are positive relationships.

Mentor: An example of a positive relationship would be between the two variables temperature and population at the beach. It is commonly known that as the weather gets warmer more people go to the beach, right? This means that as the temperature increases the amount of people at the beach will increase. This also means that as the temperature decreases there are fewer people at the beach. Despite the fact that the relationship was worded differently, the graph will still look the same for both and it is representing the same situation. Both of these situations are positive relationships because as one variable either decreases or increases the other variable does the same. Now, can you give me an example of what you would imagine a negative relationship to be?

Student: Well, now that I know what makes a relationship positive I can make a guess based off of that. I think two variables would have a negative relationship if when one variable either decreases or increases the other variable does the opposite.

Mentor: You're right! Can you think an example?

Student: Um, the more I go jogging the less time it will take me to run a mile.

Mentor: Yes! Often as the amount of time you exercise increases, the less time it takes to run a mile. What are the two variables?

Student: How long it takes me to run a mile would be one variable, and how often I jog would be the other variable.

Mentor: Very good! Now, since bivariate data focuses on a relationship between two variables there often will be one variable that is assumed to be the variable that is in control of the other variable. In the example you provided how much you jog controls the amount of time it takes you to run a mile. Therefore, how long it takes you to run a mile is dependent on how much you go jogging. There are names for both of these variables: one is an independent variable (in this case this would be the amount of time you spend jogging) and one is the dependent variable (in this case it would be how long it takes you to run a mile). Now what do you think would be the independent and dependent variable for the beach example I gave earlier?

Student: Well, the warmer it gets the more people that go to the beach. So, the temperature controls the population and the amount of people that go is dependent on how warm it is at the beach. This means that the temperature is the independent variable and the population at the beach is the dependent variable.

Mentor: Exactly! You can use the Regression activity to plot and view the relationship between the independent and dependent variables in a situation. The independent variable should be along the x-axis and the dependent variable should be along the y-axis.

Student: Cool, I now know how to determine whether a bivariate data set represents a positive or negative correlation. I can even determine which variables in a bivariate data set are independent and which are dependent.