Question

Chapter 14 Assignment An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation. N 8. 9. 10. Production Volume (units) Total Cost ($) 400 3,900 450 4,900 550 5,300 600 5,800 6,300 750 6,900 a. Compute bi and bo (to 1 decimal). bo Complete the estimated regression equation (to 1 decimal). y = + x b. What is the variable cost per unit produced to 1 decimal)? C. Compute the coefficient of determination (to 3 decimals). Note: report r2 between 0 and 1. What percentage of the variation in total cost can be explained by the production volume (to 1 decimal)? d. The company's production schedule shows 500 units must be produced next month. What is the estimated total cost for this operation (to the nearest whole number)?

Answer 1

a) From the give data

S.No.	Production (X)	Total Cost (Y)	X^2	Y^2	XY
1	400	3900	160000	15210000	1560000
2	450	4900	202500	24010000	2205000
3	550	5300	302500	28090000	2915000
4	600	5800	360000	33640000	3480000
5	700	6300	490000	39690000	4410000
6	750	6900	562500	47610000	5175000
Total:	3450	33100	2077500	188250000	19745000

Means - ΣΕ 3450 = 575 Meany - Σ' 33100 = 5516.6667 nΣαν - (Σχ)(Σ) byx = ηΣx? - (Σχ) 6 - 19745000 - 3450 - 33100 6 - 2077500 - (3450) 118470000 - 114195000 12465000 - 11902500 4275000 - 562500 = 7.6

Regression Line y on x y- j = byx (x - 1) y - 5516.6667 = 7.6(x - 575) y - 5516.6667 = 7.6x - 4370 y = 7.6x - 4370 + 5516.6667 y = 7.6x + 1146.6667

Answers:

b0 = 1146.7

b1 = 7.6

The regression equation is

Y-hat = 7.6X + 1146.7

b) Slope = $ 7.6

c) Correlation Coefficeint:

Correlation coefficient r: 2 - Σy - Σχ. Σν γη. Σx- (Σκ). - Σ2 - (Σ» 6 - 19745000 - 3450 - 33100 6 - 2077500 - (3450)2 - 6 - 188250000 - (33100) 118470000 - 114195000 12465000 - 11902500 - 1129500000 - 1095610000 4275000 562500 - 33890000 4275000 750 - 5821.5118 4275000 * 4366133.8733 - 0.9791

Correlation Deterimination: r2 = 0.97912 = 0.959

The percentage of variation in total cost is explained by the production volume is 95.8%

d) Given X = 500

Y-hat = 7.6*500 + 1146.7

Y-hat = $ 4947