Intervals constructed about the predicted value of y, at a given level of x, that are used to measure the accuracy of a single individual’s prediction are called___________intervals for a(n)_________response.

Verified step by step guidance

1. Understand that the problem is asking for the name of the type of interval used to measure the accuracy of a single individual's predicted value of \( y \) at a given \( x \).
2. Recall that in regression analysis, there are two common types of intervals related to predictions: confidence intervals and prediction intervals.
3. Recognize that confidence intervals estimate the mean response (average \( y \)) at a given \( x \), while prediction intervals estimate the range for an individual response (a single \( y \) value) at that \( x \).
4. Therefore, the intervals used to measure the accuracy of a single individual's prediction are called prediction intervals.
5. Finally, note that these prediction intervals are constructed for a quantitative (numerical) response variable \( y \).

Key Concepts

Prediction Intervals

Prediction intervals provide a range within which a single new observation is expected to fall, given a specific value of the predictor variable. They account for both the uncertainty in estimating the mean response and the variability of individual outcomes, making them wider than confidence intervals.

Response Variable

The response variable, often denoted as y, is the outcome or dependent variable in a regression model. It represents the value we aim to predict or explain based on one or more predictor variables.

Regression Analysis

Regression analysis models the relationship between a dependent variable and one or more independent variables. It allows us to predict the response variable's value and quantify the uncertainty around these predictions using intervals.