Which of the following statements about leverage in a linear model is true?

In the context of leverage within a linear regression model, the concept refers to how much influence a particular data point has on the fitted values.

The statement that the leverage for each observation must be between 1/n and 1 is indeed accurate. In a linear regression model, leverage values are derived from the hat matrix, which transforms the observed response values into predicted values. The diagonal elements of the hat matrix (which correspond to the leverage values) range from 0 to 1. Given there are n observations, the average leverage is equal to 1/n, meaning that values for individual observations can vary but must fall within this range.

This foundational understanding of leverage helps illustrate why the other statements are not true. The assertion that the sum of n leverages in a linear model must equal the number of explanatory variables is incorrect; instead, the sum of all leverage values equals the number of parameters being estimated in the model, including the intercept. Additionally, a variance inflation factor (VIF) of zero would imply no variance in the explanatory variable, which is not feasible, as uncorrelated explanatory variables would have a VIF of 1 rather than zero.

Therefore, the correct statement about leverage ensures the understanding of its role in