F-Test (ANCOVA)

The test statistic is:

$f = \frac{\sum_{i = 1}^{n} w_{i} ({\hat{y}}_{i} - \bar{y})^{2} / d f_{1}}{\sum_{i = 1}^{n} w_{i} (y_{i} - {\hat{y}}_{i})^{2} / d f_{2}}$

where:

y_{i}

is the

i

th of

n

observed values of a numeric variable,

{\hat{y}}_{i}

is a value fitted by weighted least squares,

d f_{1} = k

,

k

is the number of independent variables in the weighted least squares (excluding the constant),

d f_{2} = \sum_{i = 1}^{n} w_{i} - k - 1

,

w_{i}

p \approx \Pr (F_{d f_{1}, d f_{2}} \geq f)

.

See also