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SAS FAQ
How to compute Mahalanobis distance?

The relationship between Mahalanobis distance and hat matrix diagonal is as follows.

Based on this formula, it is fairly straightforward to compute Mahalanobis distance after regression. Here is an example using the stackloss data set.

data stackloss;
input x1 x2 x3 y;
datalines;
  80  27  89  42
  80  27  88  37
  75  25  90  37
  62  24  87  28
  62  22  87  18
  62  23  87  18
  62  24  93  19
  62  24  93  20
  58  23  87  15
  58  18  80  14
  58  18  89  14
  58  17  88  13
  58  18  82  11
  58  19  93  12
  50  18  89   8
  50  18  86   7
  50  19  72   8
  50  19  79   8
  50  20  80   9
  56  20  82  15
  70  20  91  15
;
run;
proc reg data = stackloss;
  model y = x1-x3 /influence;
  ods output  OutputStatistics = hat;
run;
quit;
data mahal;
  set hat;
  mahalanobis = sqrt((hatdiagonal-1/21)*20);
run;
proc print data = mahal;
var mahalanobis;
run;

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