Which of the following graphs shows a strong positive association between the variables 𝑚 and 𝑛?
All four of the graphs have the variable 𝑚 on the 𝑥-axis and the variable 𝑛 on the 𝑦-axis. When dealing with scatter graphs or scatter plots such as these, the association is known as the correlation. The correlation can be positive, negative, or zero, depending on whether we can draw a line of best fits and the direction of this line. In option D, the points are random. And we are unable to draw a line of best fits. We can, therefore, say that there was zero or no correlation between the variables 𝑚 and 𝑛.
In option C, we can draw a line of best fit, as shown on the graph. Our line of best fit has roughly the same number of points above and below the line. As the line slopes upwards, the correlation or association is positive. As a number of the points are a significant distance away from the line of best fit, this is a weak, positive correlation. We can also draw a line of best fit for graph B. However, this slope’s downwards. As the line slopes downwards. This is a negative correlation. All of the points are close to this line of best fit. Therefore, there is a strong negative correlation between the variables 𝑚 and 𝑛.
Option A has a line of best fit similar to option C. As it slopes upwards. This indicates a positive correlation. As all the points on the scatter graph are close to this line. We have a strong positive correlation. We can, therefore, conclude that graph A has a strong positive association between the variables 𝑚 and 𝑛. The line of best fit slopes upwards from left to right. And all of the points are close to this line.