How to Test for Co-integration with the Augmented Dickey-Fuller Test?


Hi everyone.
The table above contains two example factories that I would like to test for cointegration using the augmented dickey-fuller test. I intentionally use this short time series because I want to do the calculations by hand. Below you will see my attempt to carry out this procedure and the output from excel. I am seeking verification of the correct procedure steps to take for this example. Am I using the correct figures in my calculations? I would appreciate any help on this.

Objective: To test Factory A and Factory B for cointegration using the augmented dickie fuller test. The models of the ADF I will be using are:
Type 1 Constant, no trend Δyi = β0 + β1 yi-1 + εi
Type 2 Constant and trend Δyi = β0 + β1 yi-1 + β2 i+ εi

β = X
H0: β = 0
(equivalent to φ = 1, which means there is a unit root present; implying that Factory A is NOT cointegrated with Factory B.
H1: β < 0 (equivalent to φ < 1, which implies Factory A is cointegrated with Factory B.)

Now I start the test: