What is the smallest possible value of leverage in a regression model?

In a regression model, leverage is a measure of how far an independent variable's value is from the mean of that variable. The leverage of each observation can be calculated using a specific formula related to the design matrix of the regression, where the diagonal elements of the projection matrix determine leverage values.

The smallest possible value of leverage is indeed 0. This occurs when an observation is perfectly aligned with the mean of the predictor variables, indicating that it does not contribute to the model in terms of influencing regression estimates. Since leverage is calculated based on the ratio of distances from the mean, it cannot be negative; thus, leverage values cannot fall below zero.

This understanding reinforces that leverage can have values ranging from 0 up to a maximum value, depending on how extreme the observation is relative to the overall data distribution. Values exceeding 1 are theoretically possible in scenarios where leverage points are present, but the minimum can only be 0, reflecting the baseline position where an observation does not exert influence.