Estimating the reliability of an individual forecast
Chapter 17 has indicated the kind of variability from sample to sample that may be expected in determining statistical constants, such as regression and correlation coefficients, and in fitting regression lines and curves. It has provided means of estimating, from the values obtained from a single sample, various indications of how far and how frequently the statistics from successive samples of the same size are likely to vary from the true values of the parameters in the universe from which the samples are drawn.
The practical statistician frequently has to deal with a quite different problem. Having taken a given sample, and having determined from that sample how the selected dependent variable is related to one or more independent variables, he then has the problem of drawing new observations of the same independent variable(s) from the same universe, and of estimating from those new values the most probable value of the dependent variable for the new cases. The standard error applicable to such an estimate is called the standard error of forecast. In ordinary usage, "forecast" suggests something in the future, like tomorrow's weather, or next year's corn yield. However, statisticians also use this term in connection with new observations from universes in which time is not a source of uncertainty.
For example, in a sample of children drawn at random from the school population of a given city, certain relations may be determined between their age and height and their weight. From these relations, how closely can we expect to estimate the weight of a new child, selected at random