An agent for a real estate company in a large city collected data on the sizes $(x$ in square feet$)$ and monthly rents $(y$ in dollars$)$ of a sample of eight apartments in a neighborhood. The data is shown below, along with the linear regression equation. Complete parts a through $c$ below.

$])$:$\}$

$[$ Size $(Square$ Feet$)800,1,200,1,050,1,150,2,000,650,1,250,1,050$

a$.$ Estimate the mean monthly rent for an apartment that has $1,000$ square feet.

The mean monthly rent for such an apartment is approximately $

$($Round to the nearest cent as needed.$)$