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Because that’s how you use Dickey Fuller to check unit root:
The Dickey-Fuller test estimates the equation (xt – xt-1) = b0 + (b1 - 1) * xt-1 + et and tests if H0: (b1 – 1) = 0. Using a modified t-test, if it is found that (b1–1) is not significantly different from zero, then it is concluded that b1 must be equal to 1.0 and the series has a unit root.
here g1 is equivalent to (b1-1)
The equation you mentioned still applies but to use D/F method you have to formulate this equation

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