# Converting coefficient of slope to autoregressive factor

I realize this is very fundamental. I apologize.

Is there any way to convert the coefficients from a linear model into the decay factor if i want to express it as an autoregressive model?

For a simple example, let's say i got a slope of -2 and intercept of 22 from this data:

x   y
0   22
1   20
2   18
3   16
4   14
5   12
6   10
7   8
8   6
9   4
10  2


I calculated the decay factor from this equation:

lnY(x) = -k(x-x0) + lnY(x0)

where i got -2.3026, but i cannot seem to find how to relate it to the coefficients of the linear model.

Thank you!

• In which way is this an autoregressive model? Can it be represented by something like $y_t=\varphi_0+\varphi_1 y_{t-1}+\dots+\varphi_p y_{t-p}+\varepsilon_t$ which is a general AR(p) representation? – Richard Hardy Sep 30 '19 at 12:59