11.9:
Prediction Intervals
The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
For example, consider the scatter plot of profit versus investment of a company. These two variables are positively correlated.
The predicted profit for an investment of 920,000 will yield a single value – a point estimate of the profit.
A serious disadvantage of having a point estimate is that it does not contain any information about the accuracy of the value.
So, a prediction interval is used to estimate the range within which this y-value might lie.
The prediction interval depends on the standard error of estimate – a collective measure of the spread in data points around the regression line. A lower se-value indicates data points closer to the regression line.
The standard error of estimate is used to calculate the margin of error, which provides the prediction interval for the y-value.
11.9:
Prediction Intervals
The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.
The prediction interval can be constructed with the help of the standard error of estimate – a value that indicates the spread of data points around the regression line.
This text is adapted from Openstax, Introductory Statistics, Section 8, Confidence Interval.