Very clear and helpful article, as usual. Thanks a lot!

I tried to apply the DFBETAS formula you explained in your post "Influential observations in a linear regression model: The DFBETAS statistics",
four years ago (https://blogs.sas.com/content/iml/2019/06/17/influence-regression-dfbeta.html).

I did it on a very simple fictitious dataset, limited to 2 variables (X and Y) and to 10 observations,
where one of which is an outlier without any big effect on the slope of X, and where another one is an influent observation.
I used PROC REG three times: on the whole sample, then on the same sample after having excluded the outlier,
and, finally, on the same sample after having excluded the influent observation.
Combining the relevant pieces of information (the 3 betas for X and their standard errors for the two last models)
within your DFBETAS formula, I got, for the influent observation, the same value (4.43) as the one which is
displayed in the PROC REG's Influence table; but, for the outlier, I got a value (1.317) which is very different from 7.865
(found in the SAS Influence table).
I don't understand why.
Could you tell me why and where I made an error (despite several checks)?
Many thanks

data have;
input x y;
datalines;
1 2.89
2 5.87
3 8.98
4 12.20
5 15.06
6 18.03
7 21.15
8 24.08
50 150.00
8 8.00
;
run;

proc reg data=have; * N=10;
model y = x / influence;
run;

/* Some results (only those useful for eventually applying the DFBETAS' formula) :
beta(x) = 3.01194
DFBETA(x) for the 9th observation = 7.8650
DFBETA(x) for the 10th observation = 4.4307
*/

* without the outlier;
proc reg data=have;
where x NE 50; * N=9;
model y = x ;
run;

/* Some results (only those useful for eventually applying the DFBETAS' formula) :
beta(x) = 2.08282
standard error of beta(x) = 0.70514
*/

* without the influent observation;
proc reg data=have;
where y NE 8; * N=9;
model y = x ;
run;

/* Some results (only those useful for eventually applying the DFBETAS' formula) :
beta(x) = 3.00003
standard error of beta(x) = 0.00269
*/

/* your formula:
DFBETA(x) for obs.i = ( beta(X) estimated on all 10 observations - beta(X) estimated on 10 observations except the ith)
/ standard error of the beta(X) estimated on 10 observations except the ith

Calculations: */

%LET beta_X_without_exclusions=3.01194; * from regression-without-exclusions' results;
%LET beta_X_outlier_excluded=2.08282; * from regression where the outlier is excluded;
%LET std_err_beta_X_outlier_excluded=0.70514; * same provenance;
%LET beta_X_influent_excluded=3.00003; * from regression where the influent observation is excluded;
%LET std_err_beta_X_influent_excluded=0.00269; * same provenance;
DATA _NULL_;
DFBETA_X_outlier=%SYSEVALF( (&beta_X_without_exclusions - &beta_X_outlier_excluded) / &std_err_beta_X_outlier_excluded );
PUT DFBETA_X_outlier;
DFBETA_X_influent=%SYSEVALF( (&beta_X_without_exclusions - &beta_X_influent_excluded) / &std_err_beta_X_influent_excluded );
PUT DFBETA_X_influent;
RUN;

/* LOG :
1.3176390504
4.4275092937
*/

As I apply your formula to the influent observation, I get DFBETA(x)=4.43 (same value as 4.43 in the PROC REG's Influence table).
But, applying it to the outlier, I get DFBETA(x)=1.32, which differs strongly from DFBETA(x)=7.87 displayed by the Influence table.