# Mahalanobis squared distances of Brownlee's stack loss plant operation data based only on the explanatory variates (air flow, water temperature, and acid concentration).

### Description

Mahalanobis distances were calculated using the mahalanobis R function. Under standard normal theory, these are approximately Chi-squared on 3 degrees of freedom.

### Usage

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### Format

A data frame with 21 rows and 2 variates:

- ordinary
Mahalanobis squared distances from the arithemetic mean using the eliptical contours of the sample covariance matrix.

- robust
As with distances, these are Mahalobis squared distances butnow based on robust measures of location and covariance matrix (as determined from the default covRob of the robust package).

### Details

`with(stacklossDistances, qqtest(robust,dist="chi", df=3))`

will show "outliers".

`with(stacklossDistances, qqtest(ordinary,dist="chi", df=3))`

will show "inliers".

### Source

"Statistical Theory and Methodology in Science and Engineering", K.A. Brownlee, (1960, 2nd ed. 1965), Wiley, New York pp. 491-500.