Nancy was attempting to estimate a model for her small business overhead costs; she is $99\mathrm{.}9\%$ sure that overhead costa are driven primaril by production, but she also knows that this cost isn't entirely variable, so grabbed the last $8$ months of production and overhead costs data, listed it out and plotted it as follows.

Month # of units Produced Overhead Cost

$1200$ $$2,500$

$21601750$

$32302190$

$42902790$

$53102500$

$62702750$

$72202200$

$82402980$

a$1)$ Nancy is planning to use the high$-$low method to estimate this cost function. Is it important for the data to exhibit a linear relationship when using this method?

It $\_\_\_\_\_\_($is $/$is not$)$ important for the data to exhibit a linear relationship.

b$)$ Help Nancy estimate her company's overhead cost using the high$-$low method. Write your final model in Y$=$m$($X$)+$ b format.

Y$=$$ $\_\_\_\_\_\_\_\_\_\_$ X $+$ $ $\_\_\_\_\_\_\_\_\_\_$