Question

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.

Production Volume (units)	Total Cost ($)
400	4,900
450	5,900
550	6,300
600	6,800
700	7,300
750	7,900

a. Compute b0 and b1 (to 1 decimal).



Complete the estimated regression equation (to 1 decimal).
    

b. What is the variable cost per unit produced (to 1 decimal)?


c. Compute the coefficient of determination (to 3 decimals). Note: report r^2 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

	Production Volume (X)	Total Cost (Y)	X * Y	X2	Y2
	400	4900	1960000	160000	24010000
	450	5900	2655000	202500	34810000
	550	6300	3465000	302500	39690000
	600	6800	4080000	360000	46240000
	700	7300	5110000	490000	53290000
	750	7900	5925000	562500	62410000
Total	3450	39100	23195000	2077500	2.6E+08

Part a)

Equation of regression line is Ŷ = a + bX

b = ( 6 * 23195000 - 3450 * 39100 ) / ( 6 * 2077500 - ( 3450 )²)
b = 7.6
a =( Σ Y - ( b * Σ X) ) / n
a =( 39100 - ( 7.6 * 3450 ) ) / 6
a = 2146.7
Equation of regression line becomes Ŷ = 2146.7 + 7.6 X

b0 =  a = 2146.7

b1 = b = 7.6

Part b)

Ŷ = 2146.7 + 7.6 X

Variable cost per unit production is $2146.7.

Part c)

r = 0.979

Coefficient of Determination
R2 = r² = 0.959

Explained variation = 0.959* 100 = 95.9%

Part d)

When X = 500
Ŷ = 2146.667 + 7.6 X
Ŷ = 2146.667 + ( 7.6 * 500 )
Ŷ = 5946.67 ≈ 5947