How to test significance of sum of coefficients in proc glm statement

[Noga]

I am using proc GLM statement:

proc glm data=x;

absorb cusip;

class year;

model y= a1 a2 a3 b1 b2 b3 b4 year/solution NOINT;

run;

I want to test the statistical significance of the sum b1+b3 and the sum b2+b4.

How do I do that?

[PaigeMiller]

---

@Noga wrote:

I am using proc GLM statement:

proc glm data=x;

absorb cusip;

class year;

model y= a1 a2 a3 b1 b2 b3 b4 year/solution NOINT;

run;

I want to test the statistical significance of the sum b1+b3 and the sum b2+b4.

How do I do that?

---

"Statistical significance" is only defined relative to a specific hypothesis test. You didn't state an hypothesis you are trying to test.

[Noga]

I want to test: b1+b3=0, and b2+b4=0

[Ksharp]

@Rick_SAS wrote several blogs about it .

https://blogs.sas.com/content/iml/2022/10/12/reduced-regression-tests.html

[Noga]

but he addresses proc reg, not proc glm

[Rick_SAS]

To test a hypothesis of a linear relationship between coefficients, you can use the ESTIMATE statement: SAS Help Center: ESTIMATE Statement

For example, the following DATA step simulates data from a linear regression model for which the coefficients for x1 and x3 are +2 and -2, respectively. Similarly, the coefficients for x2 and x4 are +1.5 and -1.5, respectively.  The ESTIMATE statements produce tables that show the estimate (and std error) for the differences of the coefficients:

%let N = 100;
data Full;
call streaminit(123);
do i = 1 to &N;
   x1 = rand("Normal", 25, 5);
   x2 = rand("Normal", 14, 2);
   x3 = rand("Normal", 40, 9);
   x4 = rand("Normal", 21, 7);
   eps = rand("normal", 0, 30);
   y = 17 + 2*x1 + 1.5*x2 - 2*x3 - 1.5*x4 + eps;
   output;
end;
keep x1-x4 y;
run;

proc glm data=Full;
model y = x1-x4 / solution clmparm;
estimate 'x1-x3' x1 1 x3 -1;
estimate 'x2-x4' x2 1 x4 -1;
ods select Estimates ParameterEstimates;
quit;

The results are the same as for the REG procedure, except the GLM procedure outputs the p-value as a t test statistic, whereas PROC REG uses an F test. 

[Ksharp]

Rick,
estimate 'x1-x3' x1 1 x2 -1;
should be
estimate 'x1-x3' x1 1 x3 -1;

[Ksharp]

Or you can make a new variable new=b1+b3;

and use this variable NEW to test its estimated coefficient is zero or not ,like others variables. ?

also calling @StatDave  @SteveDenham