Society of Actuaries (SOA) PA Practice Exam

What is the primary visualization technique for examining the relationship between two continuous variables?

1. Box plots

2. Scatter plots

3. Histograms

4. Line graphs

The correct answer is: Scatter plots

The primary visualization technique for examining the relationship between two continuous variables is the scatter plot. A scatter plot displays individual data points on a two-dimensional graph, with one continuous variable plotted along the x-axis and the other continuous variable plotted along the y-axis. This allows for an immediate visual inspection of how the two variables interact with each other, revealing patterns, correlations, or trends. For instance, if there is a positive linear relationship between the two variables, the points will trend upwards from left to right. Conversely, a negative relationship would show points trending downwards. Additionally, a scatter plot can help identify clusters, outliers, and the overall distribution of the data across the two variables, which is crucial for further statistical analysis. While box plots are useful for understanding the distribution of a single continuous variable, and histograms show frequency distributions, they do not effectively illustrate relationships between two variables. Line graphs can represent relationships over time but are more suitable for time series data rather than examining the direct correlation between two independent continuous variables. Thus, the scatter plot stands out as the most effective method for analyzing and visualizing the relationship between two continuous variables.