What is the Bivariate Distribution for Continuous Data
Bivariate data is data that has been collected in two variables, and each data point in one variable has a corresponding data point in the other value. We normally collect bivariate data to try and investigate the relationship between the two variables and then use this relationship to inform future decisions.
For example, we could collect data of outside temperature versus ice cream sales, or we could study height vs shoe size, these would both be examples of bivariate data. If there was a relationship showing an increase of outside temperature increased ice cream sales, then shops could use this to buy more ice cream for hotter spells during the summer.
How to represent bivariate data?
We use scatter graphs to represent bivariate data. A scatter graph of bivariate data is a two-dimensional graph with one variable on one axis, and the other variable on the other axis. We then plot the corresponding points on the graph. We can then draw a regression line (also known as a line of best fit), and look at the correlation of the data (which direction the data goes, and how close to the line of best fit the data points are).
Drawing a scatter graph
Step 1: We start by drawing a set of axis and choosing an appropriate scale for the data. Step 2 : Label the x-axis with the explanatory / independent variable (the variable that will change), and the y-axis with the response / dependent variable (the variable which we suspect will change due to the independent variable changing). Also label the graph itself, describing what the graph shows. Step 3: Plot the data points on the graph. Step 4: Draw the line of best fit, if required.
Here is a set of data relating the temperature on days in July, and the number of ice creams sold in a corner shop.
| Temperature (° C) | 14 | 16 | 15 | 16 | 23 | 12 | 21 | 22 |
| Ice cream sales | 16 | 18 | 14 | 19 | 43 | 12 | 24 | 26 |
In this case, the temperature is the independent variable, and ice cream sales are the dependent variable. This means that we plot temperature on the x-axis, and ice cream sales on the y-axis. The resulting graph should look as follows.
Graph of Ice cream sales against temperature - StudySmarter Originals
The following data represents the journey of a car with time and distance travelled measured starting from the beginning of the journey:
| Time (in hours) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Distance (km) | 12 | 17 | 18 | 29 | 35 | 51 | 53 | 60 |
In this case, time is the independent variable, and distance is the dependent variable. This means that we plot time on the x-axis, and distance on the y-axis. The resulting graph should look as follows.
Graph of distance against time - StudySmarter Originals
What is the meaning of correlation and regression for bivariate data?
Correlation describes the relationship between two variables. We describe correlation on a sliding scale from -1 to 1. Anything negative is called a negative correlation, and a positive correlation corresponds to a positive number. The closer to each end of the scale the correlation is, the stronger the relationship, and the closer to zero the correlation is, the weaker the relationship. A zero correlation means there is no relationship between the two variables. Regression is when we draw a line of best fit for the data. This line of best fit minimizes the distance between the data points and this regression line. Correlation is a measure of how close the data is to our line of best fit. If we can find a strong correlation between two variables, then we can establish they have a strong relationship, meaning that there is a good probability that one variable influences the other.
Bivariate data - Key takeaways
- Bivariate data is the collection of two data sets, where each piece of data is paired with another from the other data set
- We use a scatter graph to show bivariate data.
- The correlation between bivariate data demonstrates how strong the relationship is between two variables.
Source: https://www.studysmarter.us/explanations/math/statistics/bivariate-data/
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