Test $\beta = 1$

Question

For example, I run the following regression

Here, I can test the beta coefficient (1,21821237) as zero (i.e. $\beta=0$) by looking at p-value.

But, How can I test $\beta =1$ ?

Answer 1

The t-statistic shown in the table is for the null hypothesis that $\beta = 0$:

$$ t = \frac{\beta - 0}{S.E.(\beta)} $$

You can test the hypothesis that $\beta = 1$ with the following t-statistic:

$$ t = \frac{\beta - 1}{S.E.(\beta)} = 1.41$$

This is not significant at $\alpha = 0.05$. You can figure out this out another way without calculating the p-value - because of the duality of confidence interval computation and hypothesis testing, you can just look at the confidence interval for $\beta$. You can see that it contains 1, so the two-tailed p-value against the null hypothesis that $\beta = 1$ is going to be greater than 0.05.