What is an interval estimate of the mean value of y for a specific value of x called?

The correct answer is the confidence interval, which provides a range of values that is likely to contain the true mean of the dependent variable (y) for a specific value of the independent variable (x). In statistical analysis, particularly in regression and other estimation methods, a confidence interval quantifies the uncertainty associated with sample estimates of the population mean.

A confidence interval is determined based on the sample data and accounts for variability, offering a way to express how confident we can be that the true mean lies within the specified range. This is particularly useful when making estimates or predictions based on a limited set of data.

In contrast, the standard deviation measures the dispersion of data points around the mean, while a prediction interval estimates the range within which a new observation is expected to fall, which is broader than a confidence interval because it accounts for both the uncertainty in estimating the mean and the variability of individual observations. Confidence level, on the other hand, refers to the probability that the confidence interval actually contains the true mean. Thus, while related concepts, they serve different purposes in statistical analysis.