Do I need another variable for $\displaystyle Y_t-Y_{t-1}$ if so how is it used in the regression?
$\displaystyle Y^{*}_{i}=\alpha+\beta_{0}X_t+u_t$
$\displaystyle \begin{bmatrix} YR & Y & X\\ 1970 & 36.99 & 52.805\\ 1971 & 33.6 & 55.906\\ 1972 & 35.42 & 63.027\\ 1973 & 42.35 & 72.931\\ 1974 & 52.48 & 84.79\\ 1975 & 53.66 & 86.589\\ 1976 & 58.53 & 98.797\\ 1977 & 67.48 & 113.201 \end{bmatrix}$
$\displaystyle \begin{bmatrix} 1978 & 78.13 & 126.905\\ 1979 & 95.13 & 143.936\\ 1980 & 112.6 & 154.391\\ 1981 & 128.68 & 168.129\\ 1982 & 123.97 & 163.351\\ 1983 & 117.35 & 172.547\\ 1984 & 139.61 & 190.682\\ \end{bmatrix}$
$\displaystyle \begin{bmatrix} 1985 & 152.88 & 194.538\\ 1986 & 137.95 & 194.657\\ 1987 & 141.06 & 206.326\\ 1988 & 163.45 & 223.541\\ 1989 & 183.8 & 232.724\\ 1990 & 192.61 & 239.459\\ 1991 & 182.81 & 235.142 \end{bmatrix}$