Video Transcript
What type of correlation exists between the two variables in the shown scatter plot? Is it (A) no correlation, (B) a positive linear correlation, or (C) a negative linear correlation?
We recall that we can draw a scatter plot where we have two sets of data related to individuals or events. And we call this bivariate data. We use one set for the 𝑥-coordinates and the other for the 𝑦-coordinates and then plot all the data as points on the scatter plot. We can then examine any patterns that may emerge in the scatter plots to see if they suggest any association or relationship between the two data sets. This is known as a correlation, and we have three possibilities: a positive correlation, a negative correlation, or no correlation.
A positive correlation occurs if as the 𝑥-value increases, so does the 𝑦-value. In this case, the points generally slope from the bottom left to the top right of the scatter plot. We can then draw a line of best fit, as shown on the figure. This line of best fit will have roughly the same number of points above and below it and will follow the trend for the points. We can therefore conclude that the type of correlation shown in the scatter plot is a positive linear correlation. Therefore, the correct answer is option (B).
In negative linear correlation, we’d see the points slope downwards from left to right. In this case, as the value of 𝑥 increases, the value of 𝑦 decreases. If the scatter plot shows no or zero correlation, we will not be able to draw a line of best fit. This is because there will be no obvious relationship between the 𝑥-values and 𝑦-values. The word “linear” is important as this implies we can draw a straight line of best fit.
