What type of data analysis would use a residual?

Residuals are a key concept in regression analysis, which involves modeling the relationships between variables. When a regression model is created, it predicts the output based on input variables. The residual is the difference between the observed value and the value predicted by the model. This difference identifies how well the model fits the data. By analyzing residuals, one can assess the accuracy of the model, detect patterns that suggest a poor fit, and check for other underlying assumptions such as linearity and homoscedasticity.

In contrast, descriptive statistics primarily focus on summarizing and understanding the basic features of data through measures such as mean, median, and standard deviation, without concern for predictions. Inferential statistics involves making predictions or inferences about a population based on a sample, often using confidence intervals or hypothesis tests without directly involving residuals. Time series analysis examines data points collected or recorded at specific time intervals to identify trends, cycles, or seasonal variations, but it does not typically engage with residuals in the same way that regression analysis does.

Thus, the use of residuals is fundamentally tied to regression analysis, making it the correct answer.