Dynamic regression

Hi everybody,

i would be happy if you could help me with my statistics =)

I do a dynamic model to check the influence of the weekdays/weekend behavior in mobilitychanges based on google data.
For this i use R-Studio.
I tried as followed:
dynlm(y_w ~ L(y_w,1) + L(D,0))
y_w is my data of the mobilitiychange. D is my dummy for saturdays and sundays. I like to create a model with a autoregessive part.
Could you tell me im right with this?

How would be the formula for the schoolpaper?
Is it like: Y_t = a_0 + a_t * Y_t-1 + D_t + error_t ?

Thanks in advance.