Gives the upper and lower bounds of more than one value of a dependent variable at several levels of the independent variables at a certain confidence level.
The resulting confidence bands are known as the Working–Hotelling–Scheffé confidence bands.

University of Michigan - Ann Arbor

A method of simultaneous estimation in linear regression models.
One of the first developments in simultaneous inference, it was devised by Working and Hotelling for the simple linear regression model in 1929.
Provides a confidence region for multiple mean responses

Working-Hotelling procedure

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, pp. 3-7). New York: springer.

An Introduction to Statistical Learning with Applications in R

Conducting multiple independent-samples $$t$$-tests to compare every pair of group means in an experiment creates a statistical problem. While a single $$t$$-test has a $$5\%$$ chance of mistakenly rejecting a true null hypothesis (a Type I error), conducting several $$t$$-tests simultaneously causes this risk to compound. As more tests are run, the overall probability of mistakenly rejecting at least one true null hypothesis becomes unacceptably high, necessitating specialized statistical procedures to control the error rate.

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