Several measurements are made of the variables 𝐴 and 𝐵. The results are plotted in a graph. How are the variables correlated?
Okay, so in this graph, we see these two variables, variable 𝐴 on the vertical axis and 𝐵 on the horizontal. And there are these five data points that connect these two variables. For example, considering this point here, we see that that point corresponds to one particular value of variable 𝐵 and one value of variable 𝐴.
In this question, we want to figure out how these two variables, variables 𝐴 and 𝐵, are correlated. When we talk about correlation, it means when we change one of these factors, in this case one of the variables, how does the other variable change.
We can better understand that relationship by looking at all five of the data points that are plotted on this graph. In particular, we can draw out what’s called a line of best fit that goes through these points. A line of best fit is a line through a set of data that best represents the pattern of that data.
One way to draw a line of best fit is to draw a loop that surrounds all the data points that we want to fit. Then once we’ve done that, we draw a line that goes midway through this loop, cutting the areas above and below the line roughly in half. Using this approximate method, this then is our line of best fit. And this will help us answer the question of how our variables 𝐴 and 𝐵 are correlated.
Because as we follow our line from left to right on our graph, like this, then we see that as we increase variable 𝐵, our line tells us that we also increase variable 𝐴. We know that because the slope or the gradient of our line of best fit is positive. Our line goes up and to the right. This means that as we increase the value on our horizontal axis, in our case variable 𝐵, we also increase the value on the vertical axis, variable 𝐴.
When an increase in one variable leads to a corresponding increase in the other variable, we say that these variables are positively correlated. This means increasing one variable means the other increases as well. Or decreasing one means the other decreases. So that when one variable changes, the other changes in the same way. That’s what positive correlation means.