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	4,400
450	5,400
550	5,800
600	6,300
700	6,800
750	7,400

1. Compute b₁ and b₀ (to 1 decimal).
   b₁
   b₀
   
   Complete the estimated regression equation (to 1 decimal).
   ŷ = ____ + _____ x
2. What is the variable cost per unit produced (to 1 decimal)?
   
3. Compute the coefficient of determination (to 3 decimals). Note: report r² between 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

Computational Table:

Production Volume (units) (X)	Total Cost ($) (Y)	X2	Y2	XY
400	4,400	160000	19360000	1760000
450	5,400	202500	29160000	2430000
550	5,800	302500	33640000	3190000
600	6,300	360000	39690000	3780000
700	6,800	490000	46240000	4760000
750	7,400	562500	54760000	5550000
Total = 3450	36100	2077500	222850000	21470000

a)

For Slope:

b = 7.6

For Intercept:

a = 6017 + 7.6*575

a = 1646.7

Therefore, the least square regression line would be,

b) Variable cost per unit is given by the slope of the regression equation, coefficient of x, which is thus 7.6 dollars per unit.

C)

Correlation coefficient (r):

r = 0.979

Coefficient of Determination (R²) = 0.979² = 0.959

95.9% of the variation in total cost can be explained by the production volume.

d)

The least square regression line would be,

Replace x in the regression equation by 500