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.

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 between total cost and production volume and then answer the questions that follow.

Open spreadsheet

1. Compute b₁ and b₀ (to 1 decimal).

   b₁

   b₀

   Complete the estimated regression equation (to 1 decimal).

   =  + x

2. According to this model, what is the change in cost (in dollars) for every 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

Production Volume (units)	Total Cost ($)
400	5000
450	6000
550	6400
600	6900
700	7400
750	8000
Production Target	Est. Cost ($)
500

Answer 1

a.

Sum of X = 3450
Sum of Y = 39700
Mean X = 575
Mean Y = 6616.6667
Sum of squares (SS_X) = 93750
Sum of products (SP) = 712500

Regression Equation = ŷ = bX + a

b = SP/SS_X = 712500/93750 = 7.6

a = M_Y - bM_X = 6616.67 - (7.6*575) = 2246.7

ŷ = 7.6X + 2246.7

b. As we know slope is the unit change in y when there is a unit change in x

So here the change in cost (in dollars) for every unit produced is 7.6

c.

X Values
∑ = 3450
Mean = 575
∑(X - M_x)² = SS_x = 93750

Y Values
∑ = 39700
Mean = 6616.667
∑(Y - M_y)² = SS_y = 5648333.333

X and Y Combined
N = 6
∑(X - M_x)(Y - M_y) = 712500

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 712500 / √((93750)(5648333.333)) = 0.979

So r*2=0.958

So percentage of the variation in total cost can be explained by the production volume is 95.8%

d. For x=500, ŷ = (7.6*500) + 2246.7=6046.7=6047