Contributor
Posts: 61

interpretation of coefficients using standard deviation

I am trying to analyse my regression results and I need to interpret the economic magnitude of specific independent variable in terms of its standard deviation.

For example: Y = a + bX + u

In general, one can say that when X increases by one unit, Y is expected to increase by 'b' value.

Alternatively, one can say that when X increases by one standard deviation, Y is expected to increase by 'some' value.

How to obtain this 'some' value in SAS?

To my understanding, formulary, for std change in X, Y would change : [b*std(y)] / mean(y). I am not sure if this formula is correct.

PROC Star
Posts: 8,167

Re: interpretation of coefficients using standard deviation

If N is the number of SD from the mean of X wouldn't you want:

a + bX* (meanX+N*sdX)

?

an Example:

```data have;
input x y;
cards;
1 3
2 6
3 9
4 12
5 14
6 18
7 20
8 24
9 26
10 28
;

proc reg data=have;
model  Y=X;
run;

proc means data=have;
var x y;
run;
```

results in: MeanX=5.5  sdX=3.02765   bX=2.83636  a=.4

Thus, 2 sd above mean would be x=11.5553

.4 +2.83636*11.553=33.17499

Art, CEO, AnalystFinder.com

Posts: 3,061

Re: interpretation of coefficients using standard deviation

Alternatively, one can say that when X increases by one standard deviation, Y is expected to increase by 'some' value.

How to obtain this 'some' value in SAS?

Y increases by b * (one standard deviation of X)

--
Paige Miller
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