Leverage values in regression analyses lie in what range?

Leverage values in regression analyses lie in what range?

• A. 0 to 1
• B. -1 to 1
• C. 0 to infinity
• D. -infinity to infinity

Answer: (A)

Leverage values come from the diagonal of the hat matrix H = X(X′X)⁻¹X′ in ordinary least squares, and each h_ii measures how much observation i influences its own fitted value. Because H is a projection operator, those diagonal elements are nonnegative and cannot exceed 1, so leverage values always lie between 0 and 1. A useful context is that the sum of all leverages equals the number of parameters in the model (including the intercept), so observations with predictor values far from the rest can have larger leverage, but they still stay within the 0 to 1 range.

Leverage values come from the diagonal of the hat matrix H = X(X′X)⁻¹X′ in ordinary least squares, and each h_ii measures how much observation i influences its own fitted value. Because H is a projection operator, those diagonal elements are nonnegative and cannot exceed 1, so leverage values always lie between 0 and 1. A useful context is that the sum of all leverages equals the number of parameters in the model (including the intercept), so observations with predictor values far from the rest can have larger leverage, but they still stay within the 0 to 1 range.