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Supplemental Math: Study Aid1 chapters | 19 lessons

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Lesson Transcript

Instructor:
*Yolanda Williams*

Yolanda has taught college Psychology and Ethics, and has a doctorate of philosophy in counselor education and supervision.

A scatterplot is used to graphically represent the relationship between two variables. Explore the relationship between scatterplots and correlations, the different types of correlations, how to interpret scatterplots, and more.

Imagine that you are interested in studying patterns in individuals with children under the age of 10. You collect data from 25 individuals who have at least one child. After you've collected your data, you enter it into a table.

You try to draw conclusions about the data from the table; however, you find yourself overwhelmed. You decide an easier way to analyze the data is by comparing the variables two at a time. In order to see how the variables relate to each other, you create scatterplots.

So what is a scatterplot? A **scatterplot** is a graph that is used to plot the data points for two variables. Each scatterplot has a horizontal axis (*x*-axis) and a vertical axis (*y*-axis). One variable is plotted on each axis. Scatterplots are made up of marks; each mark represents one study participant's measures on the variables that are on the *x*-axis and *y*-axis of the scatterplot.

Most scatterplots contain a **line of best fit**, which is a straight line drawn through the center of the data points that best represents the trend of the data. Scatterplots provide a visual representation of the **correlation**, or relationship between the two variables.

All correlations have two properties: strength and direction. The **strength** of a correlation is determined by its numerical value. The **direction** of the correlation is determined by whether the correlation is positive or negative.

**Positive correlation**: Both variables move in the same direction. In other words, as one variable increases, the other variable also increases. As one variable decreases, the other variable also decreases.- I.e., years of education and yearly salary are positively correlated.

**Negative correlation**: The variables move in opposite directions. As one variable increases, the other variable decreases. As one variable decreases, the other variable increases.- I.e., hours spent sleeping and hours spent awake are negatively correlated.

What does it mean to say that two variables have **no correlation**? It means that there is no apparent relationship between the two variables. For example, there is no correlation between shoe size and salary. This means that high scores on shoe size are just as likely to occur with high scores on salary as they are with low scores on salary.

The strength of a correlation indicates how strong the relationship is between the two variables. The strength is determined by the numerical value of the correlation. A correlation of 1, whether it is +1 or -1, is a perfect correlation. In perfect correlations, the data points lie directly on the line of fit. The further the data are from the line of fit, the weaker the correlation. A correlation of *0* indicates that there is no correlation. The following should be considered when determining the strength of a correlation:

- The closer a positive correlation lies to +1, the stronger it is.
- I.e., a correlation of +.87 is stronger than a correlation of +.42.

- The closer a negative correlation is to -1, the stronger it is.
- I.e., a correlation of -.84 is stronger than a correlation of -.31.

- When comparing a positive correlation to a negative correlation, only look at the numerical value. Do not consider whether or not the correlation is positive or negative. The correlation with the highest numerical value is the strongest.
- I.e., a correlation of -.80 is stronger than a correlation of +.55.

- If the numerical values of a correlation are the same, then they have the same strength no matter if the correlation is positive or negative.
- I.e., a correlation of -.80 has the same strength as a correlation of +.80.

So what can we learn from scatterplots? Let's create scatterplots using some of the variables in our table. Let's first compare age to Internet use. Now let's put this on a scatterplot. Age is plotted on the *y*-axis of the scatterplot and Internet usage is plotted on the *x*-axis.

We see that there is a negative correlation between age and Internet usage. That means that as age increases, the amount of time spent on the Internet declines, and vice versa. The direction of the scatterplot is a negative correlation!

In the upper right corner of the scatterplot, we see *r* = -.87. Since *r* signifies the correlation, this means that our correlation is -.87.

Could we say that aging causes the study participants to use the Internet less? We cannot draw this conclusion based on our data. It is important to note that correlation does not equal causation. A correlation indicates that the two variables are related in some way. It does not tell us anything about the cause of this relationship. In order to determine if one variable causes the other, an experiment would need to be conducted.

Now let's look at the scatterplot of years of education and age at birth of first child. Years of education is plotted on the *y*-axis of the scatterplot and age at birth of first child is plotted on the *x*-axis.

By looking at the direction of the scatterplot, we see that there is a positive correlation between the two variables. As years of education increase, so does the age at which the study participant had their first child. Again, we cannot say that one variable caused the other.

In the upper right corner of the scatterplot, we see *r* = .91, which indicates that our correlation is .91. The correlation between years of education and age at birth of first child (.91) is stronger than the correlation between age and Internet usage (-.87). If we look at the line of fit, we see that the data points on the years of education and age at birth of first child are slightly closer to the line of best fit than the data points on the age and Internet use scatterplot.

You would probably not expect there to be a relationship between weight and months at current job. Let's look at a scatterplot of the two variables to see if a relationship exists.

We can see that there is no data pattern present, which is why the line of best fit is missing. We see that an increase in weight is not associated with an increase or decrease in months on the job and vice versa. There is little or no correlation between weight and months at current job.

A **scatterplot** is used to represent a correlation between two variables. There are two types of correlations: positive and negative. Variables that are positively correlated move in the same direction, while variables that are negatively correlated move in opposite directions. If there is no apparent relationship between the two variables, then there is no correlation. Scatterplots can be interpreted by looking at the direction of the line of best fit and how far the data points lie away from the line of best fit.

Accomplish the following goals when the video lesson ends:

- Know the components of a scatterplot, and identify the purpose of using one
- Differentiate between positive correlations, negative correlations and no correlations
- Determine the strength of correlation on a scatterplot
- Use the line of best fit to interpret a scatterplot

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Supplemental Math: Study Aid1 chapters | 19 lessons

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