Regression Analysis

Bogota Corporation has gathered data on its overhead activities and associated costs for the past $12$ months. Josh Hopper, from the accounting department, has convinced management that overhead costs can be better estimated and controlled if the fixed and variable components of each overhead activity are known. One such activity is the purchasing department $($receiving and reviewing purchase requisitions, issuing purchase orders, and managing vendor relationships$),$ which he believes is driven by the number of purchase orders issued. Twelve months of data have been gathered for the purchasing activity and are as follows:

$\backslash$table$[[$Month$,\backslash$table$[[$Purchase$],[$Orders$],[$Issued$]],\backslash$table$[[$Purchasing$],[$Cost$]]],[1,1,050,18,100],[2,750,15,100],[3,1,550,28,100],[4,1,250,17,100],[5,1,350,25,100],[6,1,150,21,100],[7,1,650,29,100],[8,1,450,24,100],[9,1,750,27,100],[10,950,16,100],[11,1,250,18,100],[12,1,500,18,600]]$

Assume Josh has used the method of least squares $($i$.$e$.,$ regression analysis$)$ on the purchasing data and has gotten the following results:

$\backslash$table$[[$Intercept$,$$$3,23$