Algebra Worksheets

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Positive Correlation

By Alison Rodriguez

Scatterplots are a useful tool for those interested in observing trends in data. A positive correlation is when two variables move in the same direction. Specifically, a positive correlation exists when one variable decreases as the other decreases, or one variable increases as the other increases.

Why is this concept useful?

When studying data, it is often important to see how closely related two variables are. We use the terms positive correlation to express that both variables are moving in the same direction at the same time. You can see a variety of types of positive correlation, including a strong positive or a weak positive.

Where does this concept fit into the curriculum?

7th and 8th grade, Algebra 1

How can we use positive correlation?

There are three different types of correlation you use when describing the relationship between two variables. We use scatterplots to show these relationships or associations between the two numerical variables that can be represented as a point. We can find the strength and direction of these points. Negative correlation implies that the variables are moving in different directions, positive correlation implies that the variables move in the same direction, and no correlation means that the variables are not related and the scatterplot cannot find any shape.


We can use correlation coefficients to also help describe the strength of a graph. We can categorize the strength into three options: strong, moderate, or weak. In general, we focus on strong versus weak when describing the scatterplots. The correlation coefficient, r, can also tell us how strong of a correlation the variables have. The values range from -1 to 1. A correlation of 1 means there is a perfect positive correlation and any numbers between 1 and 0 imply a positive correlation. The closer to 1, the stronger the correlation is. It is important for researchers to be able to easily see if there is a potential relationship between variables to draw conclusions about what they are studying. Keep in mind that correlation does not necessarily mean causation!





Sample Math Problems

1. The scatter plot below shows the relationship between the number of hours worked and the amount of money earned. How would you describe the relationships between the variables?

Solution:

As the number of hours worked increases, the amount of money earned in dollars also increases. This shows there is a positive correlation. When graphed, the points are very close together and would almost form a straight line. This tells you there is a strong positive correlation.


2. The following scatterplot shows the relationships between the outdoor temperature and the number of customers in an ice cream store. How would you describe the relationships between the variables?

Solution:

As the temperature increases, the number of customers also increases. However, if you were to draw in a line of best fit, the values would not be very close. Therefore this is a weak positive correlation.

3. A teacher conducted a study on her students in which she asked the number of hours the students spent studying and compared it to the overall scores. Draw a scatterplot that might represent the data collected.

Solution:

Usually, the more time spent studying, the higher the score they might receive. However, that is not true for everyone. It can be assumed this would have a positive impact, but be more of a weak positive. See the sample graph below.

4. A science class conducted an experiment that involved hearing time and water temperature. Draw a scatterplot that might represent the data collected.

Solution:

As time progresses with a constant heat source, the temperature of the water will continue to rise until it begins to boil. This relationship would be expected to have a strong positive correlation. See the sample graph below.


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Practice Math Problems

1.The scatterplot below represents the number of days compared to the height of a flower. Describe the relationship between the two variables.

2. The following scatterplot represents the relationship between the age of a vintage car and it’s associated value. Describe the relationship between the two variables.

3. A scientist was comparing the age and weight of a newborn baby over the course of one year. Draw a scatterplot that might represent the data collected and describe the relationship.

4. A pilot was tracking his flights to keep track of the number of hours in a plane compared to the number of miles flown. Draw a scatter plot to represent the data collected and describe the relationship.


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