Question

Tony has the following data concerning the prior 12 months of operations:

Pizzas Prepared Total Operating Costs October 5,513 $40,232 6,067 40,544 November December 6,690 7,000 January February 42,897 44,564 30,549 2,586 March 3,000 34,536 April 3,492 May 3,718 June 4,010 36,216 36,291 37,373 37,655 38,423 39,099 July 4,366 August 4,735 September 4,806 Total 55,983 $458,379

What is the cost function equation obtained by running a least squares reqression analysis?

If the cost function equation estimated by the high-low method: Y=22338+3.18x. Which estimation method (high-low vs. least squares) do you think provides the best fit?

Answer 1

Month	Pizzas prepared(X)	Total Cost(Y)(in $)	Square of X	X*Y(in $)
Oct	5,513	40,232	3,03,93,169	22,17,99,016
Nov	6,067	40,544	3,68,08,489	24,59,80,448
Dec	6,690	42,897	4,47,56,100	28,69,80,930
Jan	7,000	44,564	4,90,00,000	31,19,48,000
Feb	2,586	30,549	66,87,396	7,89,99,714
Mar	3,000	35,436	90,00,000	10,63,08,000
Apr	3,492	36,216	1,21,94,064	12,64,66,272
May	3,718	36,291	1,38,23,524	13,49,29,938
Jun	4,010	37,373	1,60,80,100	14,98,65,730
Jul	4,366	37,655	1,90,61,956	16,44,01,730
Aug	4,735	38,423	2,24,20,225	18,19,32,905
Sep	4,806	39,099	2,30,97,636	18,79,09,794
Total	55,983	4,59,279	28,33,22,659	2,19,75,22,477
	Unit Variable Cost (b) = nΣxy − (Σx)(Σy) /nΣx^2 − (Σx)^2		Total Fixed Cost (a) = Σy − bΣx / n
So here n =12 ,Σx =55,983, Σy =459,279, Σx^2=28,33,22,659 ,Σxy =2,19,75,22,477
Variable cost per unit(b) =12*1,19,75,22,477 - (55,983*459,279) / 12*28,33,22,659 - 55,983^2
Variable cost per unit(b) =26,37,02,69,724 - 25,71,18,16,257 / 3,39,98,71,908 - 3,13,40,96,289
Variable cost per unit(b) =65,84,53,467 / 26,57,75,619 =$2.48
Total Fixed cost =459,279 - ($2.48*55,983) / 12
Total Fixed cost =(459,279 - 138,838) / 12
Total Fixed cost =$320,441 /12 =$26,703
The cost volume formula is:
y =$26,703 + $2.48X
Since the Total cost in high low method is lesser than Regression method,hence High-low method is more prefferred