Question

How do confidence intervals differ from prediction intervals? How are these two intervals affected by the distance value?

Answer 1

Confidence interval & Prediction interval, both are mutually related & based upon sample data but there is some difference between them. Here, I am going to explain both:

Confidence interval calculations take sample data and produce a range of values that likely contains the population parameter that you are interested in. For example, the confidence interval of the mean (5,6) suggests that the population mean is likely to be between 5 and 6.

Prediction intervals are intervals which are mostly used in forecasting & prediction of data & it is mostly used in regression theory. These intervals predict the value of the dependent variable given specific settings of the independent variables. It is a range that likely contains the value of the dependent variable for a single new observation given specific values of the independent variables.

Difference between confidence interval & prediction interval by the distance value is

The confidence interval tells us about the likely location of the true population parameter whereas the prediction interval tells us about the distribution of values, not the uncertainty in determining the population mean.