topic Re: get coefficient of a Multiple Regression in SAS Programming

get coefficient of a Multiple Regression

Alexxxxxxx — Sat, 11 Feb 2023 12:09:51 GMT

Hello all,

May I ask a question about OLS regression (Y=alpha+a1*X1+a2*X2+a3*X3)?

In Table1, I have Y, X1, X2 and X3 for each Firm_ID on each Date,

Table 1
Firm_ID	Year	Date	Y	X1	X2	X3
1	1994	02/17/1994	371	-445	2138	-196
1	1994	02/18/1994	3248	-454	3457	2389
1	1994	02/22/1994	1678	5992	-62	1747
1	1995	02/17/1995	-11	-12	1848	-263
1	1995	02/18/1995	-3803	-1253	3372	1806
1	1995	02/22/1995	4456	3632	-21	291
2	1994	02/17/1994	-8995	3925	8434	-326
2	1994	02/18/1994	229	-506	-235	2486
2	1994	02/22/1994	208	-184	-594	-204
2	1995	02/17/1995	-12	-223	4152	-32
2	1995	02/18/1995	1578	4563	369	-88

I expect to get alpha, a1, a2 and a3 for each Firm_ID in each year (e.g., Table2).

Table 2
Firm_ID	Year	alpha	a1	a2	a3
1	1994	alpha 1	Aaa1	Aaa2	Aaa3
1	1995	alpha 2	Bbb1	Bbb2	Bbb3
2	1994	alpha 3	Ccc1	Ccc2	Ccc3
2	1995	alpha 4	Ddd1	Ddd2	Ddd3

Could you please give me some advice?

Many thanks in advance.

data table1;
infile cards dsd dlm=",";
input
firm_id :$5.
Year :8.
Date :MMDDYY10.
Y :8.
X1 :8.
X2 :8.
X3 :8.
;
cards;
1,1994,02/17/1994,371,-445,2138,-196  
1,1994,02/18/1994,3248,-454,3457,2389
1,1994,02/22/1994,1678,5992,-62,1747  
1,1995,02/17/1995,-11,-12,1848,-263    
1,1995,02/18/1995,-3803,-1253,3372,1806
1,1995,02/22/1995,4456,3632,-21,291   
2,1994,02/17/1994,-8995,3925,8434,-326
2,1994,02/18/1994,229,-506,-235,2486  
2,1994,02/22/1994,208,-184,-594,-204  
2,1995,02/17/1995,-12,-223,4152,-32   
2,1995,02/18/1995,1578,4563,369,-88   
;;;
run;

Re: get coefficient of a Multiple Regression

PaigeMiller — Sat, 11 Feb 2023 17:45:02 GMT

In this simple example, you cannot estimate the coefficients of three independent variables since you only have 3 data points for each year/firm combination. To fit a model with 3 independent variables, you would need 4 or more data points for each year/firm combination.

Assuming your have more data, you can estimate the regression coefficients using PROC REG

proc reg data=table1 outest=coefficients;
    by firm_id year;
    model y=x1 x2 x3;
run;

If you have lots of firms and years, this could take a very long time, and then you would probably wise to turn off the ODS GRAPHICS and turn off output to HTML before you run this, which will speed this up, and then view the coefficients in the output data set. So you would place these commands before PROC REG.

ods graphics off;
ods html select none;

From now on, no need to show us a screen capture or table of the data, all we need is the SAS data step code which you also provided.

Re: get coefficient of a Multiple Regression

sbxkoenk — Sat, 11 Feb 2023 21:54:54 GMT

Hello @Alexxxxxxx ,

Are you sure you don't need a PANEL DATA REGRESSION?

Your firms are cross-sections and your years make time series for output and inputs.

Time Series Cross-Sectional regression (=panel data regression) can be done with the old procedure PROC TSCSREG (SAS/ETS).
Newer and better procedures are PROC PANEL and PROC CPANEL (SAS VIYA Econometrics using CAS engine).

This way, you get one big model instead of several independent models.

BR,

Koen