# Clarifying Elder & Kennedy 2001 Case 3, how to test for the presence of intercept?

I am attempting to follow the unit root testing strategy for Case 3 as per [Elder & Kennedy 2001].

After failing to reject there is no unit root, I wish to test for the presence of an intercept. What does "from regressing $\Delta(y_t)$ only on an intercept" (at the bottom of page 143) mean?

Is testing of the following equation correct?

$H_0$ : There is no intercept, $H_1$ : There is an intercept.

$$\Delta(y_t) - 1 = 0$$

or in R programming,

lm(diff(y)~1)