Which statement about leverage in a linear model is true?

Leverage in the context of a linear model refers to how much an individual observation can influence the overall fit of the model. Each observation has an associated leverage statistic that indicates its influence on the predicted values. This statistic is derived from the design matrix of the model.

The correct statement indicates that the leverage for each observation must fall within the range of 1/n to 1. Here’s why this is true:

1. The value 1/n signifies the average leverage, where n is the total number of observations. Since leverage is calculated based on the distances of the predictor variable values from the mean of the predictor space, the maximum leverage for any single observation cannot exceed 1. This is because leverage is bounded by the size of the sample and the contribution of each observation to the overall fit must be reasonable relative to the total number of observations.

2. Leverage values that are below 1/n indicate that an observation is not particularly influential in terms of fitting the linear regression model, as they contribute less relative to the overall sample size. Conversely, values that exceed 1 would not be possible since they would imply an impossible degree of influence, exceeding the average.

This understanding of leverage is critical in evaluating influence and assessing potential outliers within the