# Solved – In SAS, how to perform a one sided test of the coefficient in a linear regression

Say I have fitted a model using

``proc reg data = data;    model a = b;  run; ``

How do I test if the coefficient of b is, say, less than 1?

Contents

This is in no way specific to SAS but if you have the coefficient estimate, \$hat{beta}\$ and the standard error, \$s\$, and you want to test the null hypothesis \$H_{0} : beta = beta_{0}\$ then the test statistic is

\$\$ T = frac{ hat{beta} – beta_{0} }{ s } \$\$

which has a \$t\$-distribution with \$n-2\$ degrees of freedom, denoted by \$t_{n-2}\$. To do a 1-sided test of "greater than" calculate the area to the right of \$T\$ under the \$t_{n-2}\$ distribution. Similarly, to do a one-sided test of "less than", calculate the area to the left. To do a two-sided test, find twice the area to the left of \$-|T|\$. I'm no SAS expert but I believe the areas under the \$t\$-distribution can be calculated using the tinv() command.

Rate this post