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Explanatory leverage in a straight-line fit

For a straight-line intercept fit, hi=1/n+(xi−x̄)²/Sxx.

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Define the explanatory-side quantity

Leverage depends on the observed X values, their mean and centered squared sum. It does not use a point’s Y residual by itself. A distant explanatory value can be accurately observed and informative.

Read the intercept-model expression

hi=1n+(xi−xˉ)2Sxxh_i=\frac{1}{n}+\frac{(x_i-\bar{x})^2}{S_{xx}}

For this two-parameter equal-weight straight-line fit with Sxx>0.

Inspect the original benchmark record

With n=5, x̄=0 and Sxx=10 in percentage-point units, endpoint benchmark values −2 and +2 have leverage 0.6. Values −1 and +1 have 0.3; zero has 0.2. These values sum to two, the number of fitted coefficients.

Keep leverage and data quality separate

A leverage value describes potential fitting sensitivity, not proof that an observation is erroneous or should be deleted. Residual size, source evidence and the estimation purpose also matter. The calculator plots the record but does not automatically screen or remove points.

Further references