Bivariate data is the name for numerical data consisting of two sets of individual data. We are often interested in whether there seems to be any connection between the two sets of data. A scattergraph (or scatterplot) provides a visual representation of the numerical data which can help to determine whether there is a relationship between the two sets.
The explanatory variable is plotted on the horizontal axis and the response variable is plotted on the vertical axis. A single data point in a bivariate data set is written in the form (x,y), with the first number x being the explanatory variable and the second number y being the response variable.
When describing the correlation of the two variables in a scattergraph, we want to describe the strength of the correlation and the direction of the correlation.
To describe the strength of a correlation, we use the words perfect, strong, weak, and no correlation. Perfect correlation means that the points in the scattergraph form a perfect line, and no correlation means that the points form no trend at all.
To describe the direction of a correlation, we use the words positive and negative correlation. Positive correlation means that as the explanatory variable increases, the response variable also increases. Negative correlation means that as the explanatory variable increases, the response variable decreases. Even without a scattergraph, we can use these words to describe the relationship between two variables.
Here are some examples of what each correlation description looks like.
Positive correlations
Negative correlations
The following table shows the number of traffic accidents associated with a sample of drivers of different age groups.
Age | Accidents |
---|---|
20 | 41 |
25 | 44 |
30 | 39 |
35 | 34 |
40 | 30 |
45 | 25 |
50 | 22 |
55 | 18 |
60 | 19 |
65 | 17 |
Which of the following scatter plots correctly represents the above data?
Is the correlation between a person's age and the number of accidents they are involved in positive or negative?
Is the correlation between a person's age and the number of accidents they are involved in strong or weak?
Which age group's data represent an outlier?
Consider the two variables: time spent studying and exam performance.
Is there likely to be a relationship between the two?
Do you think the correlation is positive or negative?
When describing the correlation of the two variables in a scattergraph, we want to describe the strength of the correlation and the direction of the correlation.
To describe the strength of a correlation, we use the words perfect, strong, weak, and no correlation.
To describe the direction of a correlation, we use the words positive and negative correlation.