Asked by gaurang narang on May 17, 2024
Verified
The confidence interval estimate of the expected value of y will be narrower than the prediction interval for the same given value of x and confidence level.This is because there is less error in estimating a mean value as opposed to predicting an individual value.
Confidence Interval Estimate
A range of values derived from sample data that is likely to contain the value of an unknown population parameter, expressed at a given level of confidence.
Prediction Interval
An estimate of an interval in which future observations will fall, with a certain level of confidence, based on current sample data.
Expected Value
The average outcome or mean of a random variable, calculated as the sum of all possible values each multiplied by its probability of occurrence.
- Separate the concepts of confidence intervals and prediction intervals within regression analysis discussions.
Verified Answer
MS
Mason SaubertMay 23, 2024
Final Answer :
True
Explanation :
Confidence interval estimates are used to capture the true mean value of the population, whereas prediction intervals are used to capture individual values. As the error in predicting an individual value is higher compared to estimating a mean value, the prediction interval will be wider than the confidence interval estimate for the same given value of x and confidence level.
Learning Objectives
- Separate the concepts of confidence intervals and prediction intervals within regression analysis discussions.