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	4,800
450	5,800
550	6,200
600	6,700
700	7,200
750	7,800

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 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

Using the Data analysis in excel. Y value as TC and X values as production volume.
SUMMARY OUTPUT
Regression Statistics
Multiple R	0.979127
R Square	0.95869
Adjusted R Square	0.948362
Standard Error	241.5229
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	5415000	5415000	92.82857	0.000649
Residual	4	233333.3	58333.33
Total	5	5648333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept(b0)	2046.667	464.1599	4.4094	0.011606	757.9521	3335.381	757.9521	3335.381
x(b1)	7.6	0.788811	9.634759	0.000649	5.409911	9.790089	5.409911	9.790089
a) b1 = slope coefficient = 7.6
b0 = intercept = 2046.7
estimated regression:
y = 2046.7 + 7.6x
y = Total cost
x = production volume
b) variable cost (b1) = $7.6 per unit
c) r2 = 0.959.
Percentage of variation in total cost can be explained by the production volume = 95.9%
d) x = 500.
y = 2046.7 + 7.6*500 = $5846.7 = $5847