E$5-24($Algo$)$ Estimating Cost Behavior Using Least$-$Squares Regression and High$-$Low Method $[$LO $5-3,5-4]$

Tempe Office Services and Supplies $($TOSS$)$ provides various products and services in the Tempe Research Park, home to numerous high$-$tech and bio$-$tech companies. Making color copies is one of its most popular and profitable services. The controller performed a regression analysis of data from the Color Copy Department with the following results:

Intercept $510\mathrm{.}04788$

R$-$squared $0\mathrm{.}947346$

Number of observations $6$

X coefficient $0\mathrm{.}059078$

The regression output was based on the following data:

Month Number of Color Copies Color Copy Department Costs

July $20,900$ $ $1,735$

August $24,9002,010$

September $20,8501,710$

October $24,0501,900$

November $20,4001,740$

December $20,5001,740$

Required:

$1.$ What is the variable cost per color copy for TOSS?

$2.$ What is the fixed cost for the Color Copy Department?

$3.$ Based on the regression output obtained by the controller, what cost formula should be used to estimate future total costs for the Color Copy Department? Enter answer as an equation in the form of y $=$ a $+$ bx$.$

$5-$a$.$ Use the high$-$low method to estimate the variable and fixed costs for the Color Copy Department.

$5-$b$.$ What cost formula should be used based on your analysis? Enter answer as an equation in the form of y $=$ a $+$ bx$.$

$6.$ If $23,500$ copies are made during January, what is the total cost predicted by each method?