Leverage
h = leverage(data)
h = leverage(data,model)
h = leverage(data) finds
the leverage of each row (point) in the matrix data for
a linear additive regression model.
h = leverage(data, finds
the leverage on a regression, using a specified model type, where model)model can
be one of the following:
'linear' - includes constant and
linear terms
'interaction' - includes constant,
linear, and cross product terms
'quadratic' - includes interactions
and squared terms
'purequadratic' - includes constant,
linear, and squared terms
Leverage is a measure of the influence of a given observation on a regression due to its location in the space of the inputs.
One rule of thumb is to compare the leverage to 2p/n where n is the number of observations and p is the number of parameters in the model. For the Hald data set this value is 0.7692.
load hald h = max(leverage(ingredients,'linear')) h = 0.7004
Since 0.7004 < 0.7692, there are no high leverage points using this rule.
[Q,R] = qr(x2fx(data,'model'),0);
leverage = (sum(Q'.*Q'))'
[1] Goodall, C. R. “Computation Using the QR Decomposition.” Handbook in Statistics. Vol. 9, Amsterdam: Elsevier/North-Holland, 1993.