Final answer:
The correct option is 'e. regression analysis,' which is a statistical tool used to study and quantify the relationship between a dependent variable (Y) and one or more independent variables (X).
Step-by-step explanation:
The correct answer is option e. regression analysis. When a researcher uses regression analysis to study relationships between countries, they are indeed assuming that there is a relationship between a dependent variable, often referred to as Y, and one or more independent variables, known as X. This statistical method is used to analyze the strength and direction of the relationship between variables. For example, using regression analysis with GIS software can help determine how various factors, such as ethnicity, income, or access to parks, influence obesity rates in a neighborhood. Regression analysis seeks to understand not just if there is a relationship, but also how strong that relationship is and which factors are the most influential.
Regression analysis can be employed to evaluate various relationships. For instance, one might use it to assess the relationship between the area of a state and its ranking, or to analyze whether the number of letters in a state's name is related to when it entered the Union. The independent variable is the predictor, such as the year of statehood, and the dependent variable is the outcome that might be affected by it, such as the state name length. Scatter plots, correlation coefficients, and the least-squares line are tools used in this analysis to draw insights.