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)?
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 $2146.7.
Part c)
r = 0.979
Coefficient of Determination
R2 = r2 = 0.959
Explained variation = 0.959* 100 = 95.9%
Part d)
When X = 500
Ŷ = 2146.667 + 7.6 X
Ŷ = 2146.667 + ( 7.6 * 500 )
Ŷ = 5946.67 ≈ 5947
An important application of regression analysis in accounting is in the estimation of cost. By collecting...
An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation. Production Volume (units) Total Cost ($) 400 3,500 450 4,500 550 4,900 600 5,400 700 5,900...
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 ($) 400 3,700 450 4,700 550 5,100 600 5,600 700 6,100...
An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation. Production Volume (units) Total Cost ($) 400 3,500 450 4,500 4,900 5,400 5,900 6,500 a. Compute...
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 ($) 400 4,000 450 5,000 550 5,400 5,900 700 6,400 750...
An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation.a. Compute b1 and bo (to 2 decimals if necessary) Complete the estimated regression equation (to 2 decimals...
An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation. Production Volume (units) Total Cost ($) 400 3,900 450 5,100 550 5,400 600 5,900 700 6,400...
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 ($) 400 3800 500 4300 600 5300 650 5900 750 6300...
Chapter 14 Assignment An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation. N 8. 9. 10. Production Volume (units) Total Cost ($) 400 3,900 450...
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. In the Microsoft Excel Online file below you will find a sample of production volumes and total cost data for a manufacturing operation. Conduct a regression analysis to explore the relationship...
21. 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 produc- tion volumes and total cost data for a manufacturing operation. Production Volume (units) 400 450 550 600 700 750 Total Cost ($) 4000 5000...