Video Transcript
Which of the following scatter graphs represents the strongest negative correlation between two variables? Is it graph (A), graph (B), graph (C), graph (D), or graph (E)?
We begin by recalling that we can identify whether a scatter graph has positive, negative, or zero correlation by drawing a line of best fit. A line of best fit refers to a line through a scatter graph of data points that best expresses the relationship between those points. We have drawn an example of this line of best fit on each of our five graphs. When this line slopes upwards from left to right, we have a positive correlation. As we are looking for a negative correlation, we can rule out options (A) and (B). Options (C) and (D) do show a negative correlation between the two variables as our line slopes downwards from left to right.
If our line of best fit is horizontal or vertical as in option (E), there is no correlation. This is due to the fact that if we know the 𝑥-value, in this case six, it doesn’t help us estimate or work out the 𝑦-value. From the scatter graph, we see that an 𝑥-value close to six represents 𝑦-values from one to 10. As there is no correlation in this graph, we can rule out option (E). We are trying to find the graph with the strongest negative correlation. This occurs when the set of data points are closest to the line of best fit.
Option (D) represents a strong negative correlation, whereas option (C) represents a weak negative correlation. This is because many of the points in scatter graph (C) are a significant distance away from the line of best fit. We can therefore conclude that the correct answer is option (D).
