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	4,700
450	5,700
550	6,100
600	6,600
700	7,100
750	7,700

1. Compute b₁ and b₀ (to 1 decimal).
   b₁  
   b₀  
   
   Complete the estimated regression equation (to 1 decimal).
   =  +  x
   
2. What is the variable cost per unit produced (to 1 decimal)?
   $
   
3. Compute the coefficient of determination (to 3 decimals). Note: report r²between 0 and 1.
   r² =  
   
   What percentage of the variation in total cost can be explained by the production volume (to 1 decimal)?
   %
   
4. 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
	400	4700	1880000	160000	22090000
	450	5700	2565000	202500	32490000
	550	6100	3355000	302500	37210000
	600	6600	3960000	360000	43560000
	700	7100	4970000	490000	50410000
	750	7700	5775000	562500	59290000
Total	3450	37900	22505000	2077500	245050000

Equation of regression line is


b = 7.6

a =( 37900 - ( 7.6 * 3450 ) ) / 6
a = 1946.7
Equation of regression line becomes

b0 = a = 1946.7

b1 = b = 7.6

What is the variable cost per unit produced

$7.6

r = 0.979

Coefficient of Determination

Explained variation = 0.959* 100 = 95.9%
Unexplained variation = 1 - 0.959* 100 = 4.1%

When X = 500
= 1946.667 + 7.6 X
= 1946.667 + 7.6 * 500
= 5746.67

= 5747