Society of Actuaries (SOA) PA Practice Exam

What should be assessed when analyzing the relationship between a Factor predictor variable and a Continuous target variable?

1. Histograms of the continuous target

2. Box plots and tables summarizing the target

3. Bar charts of factor levels

4. Scatter plots of factor vs target

The correct answer is: Box plots and tables summarizing the target

When analyzing the relationship between a Factor predictor variable and a Continuous target variable, it is essential to focus on summarizing the continuous target variable across the levels of the factor. This is accomplished effectively through the use of box plots and tables. Box plots provide a visual representation that displays the central tendency, variability, and any potential outliers in the continuous target variable for each level of the factor. This gives insights into how the median values of the target differ across the categories of the factor, as well as the range and distribution within each category. Additionally, tables summarizing the target variable enable a detailed quantitative analysis by presenting key statistics such as means, medians, standard deviations, and counts for the target variable across each factor level, facilitating a deeper understanding of relationships and differences. In this context, while histograms provide helpful information about the distribution of the continuous target variable, they do not convey how that distribution varies by the factor levels. Bar charts of factor levels focus more on the counts or averages of the target but do not address variability or distribution effectively. Scatter plots, while useful for visualizing relationships in some contexts, do not appropriately represent the categorical nature of the factor predictor against the continuous target in a meaningful way when multiple factor levels exist