Garfield Company manufactures a popular brand of dog repellant known as DogGone It$,$ which it sells in gallon$-$size bottles with a spray attachment. The majority of Garfield$$s business comes from orders placed by homeowners who are trying to keep neighborhood dogs out of their yards. Garfield$$s operating information for the first six months of the year follows:

Month Number of Bottles Sold Operating Cost

January $1,000$ $ $10,630$

February $1,46015,620$

March $1,70015,940$

April $2,47019,720$

May $3,47027,870$

June $3,80034,800$

Required:

$3.$ Using the high$-$low method, calculate Garfield$$s total fixed operating costs and variable operating cost per bottle.

$4.$ Perform a least$-$squares regression analysis on Garfield$$s data.

$5.$ Determine how well this regression analysis explains the data.

$6.$ Using the regression output, create a linear cost equation $($y $=$ a $+$ bx$)$ for estimating Garfield$$s operating costs.