I am trying to estimate a partial adjustment model but my book doesn't give any guidance.
Do I need another variable for $Y_t-Y_{t-1}$ if so how is it used in the regression?

$
Y^{*}_{i}=\alpha+\beta_{0}X_t+u_t
$

The data set I am working with is:
$
\begin{bmatrix}
YR & Y & X\\
1970 & 36.99 & 52.805\\
1971 & 33.6 & 55.906\\
1972 & 35.42 & 63.027\\
1973 & 42.35 & 72.931\\
1974 & 52.48 & 84.79\\
1975 & 53.66 & 86.589\\
1976 & 58.53 & 98.797\\
1977 & 67.48 & 113.201
\end{bmatrix}
$

$
\begin{bmatrix}
1978 & 78.13 & 126.905\\
1979 & 95.13 & 143.936\\
1980 & 112.6 & 154.391\\
1981 & 128.68 & 168.129\\
1982 & 123.97 & 163.351\\
1983 & 117.35 & 172.547\\
1984 & 139.61 & 190.682\\
\end{bmatrix}
$

$
\begin{bmatrix}
1985 & 152.88 & 194.538\\
1986 & 137.95 & 194.657\\
1987 & 141.06 & 206.326\\
1988 & 163.45 & 223.541\\
1989 & 183.8 & 232.724\\
1990 & 192.61 & 239.459\\
1991 & 182.81 & 235.142
\end{bmatrix}
$