What type of analysis is used to examine the relationships and impacts of variables in quantitative data?

Regression analysis is the correct choice because it specifically focuses on understanding the relationships between dependent and independent variables in quantitative data. This method allows researchers to determine how changes in predictor variables affect an outcome variable, providing insights into not just the strength but also the nature of the relationships between variables. It can identify trends, make predictions, and support causal inferences by accounting for different factors’ influences simultaneously.

In contrast, descriptive statistics summarize and describe the main features of a dataset but do not analyze relationships or impacts. Correlation analysis measures the strength and direction of the association between two variables but doesn't imply causation or account for other influencing factors. Qualitative coding is a technique used primarily for analyzing non-numerical data, focusing on themes or patterns in text rather than the relationships inherent in quantitative data. Hence, regression analysis stands out as the most comprehensive method for examining the relationships and impacts of variables in quantitative research.