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	4,500
450	5,500
550	5,900
600	6,400
700	6,900
750	7,500

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

a.

Sum of X = 3450
Sum of Y = 36700
Mean X = 575
Mean Y = 6116.6667
Sum of squares (SS_X) = 93750
Sum of products (SP) = 712500

Regression Equation = ŷ = bX + a

b1 = SP/SS_X = 712500/93750 = 7.6

b0 = M_Y - bM_X = 6116.67 - (7.6*575) = 1746.7

ŷ = 7.6X + 1746.7

b. Variable cost per unit is the slope so answer here is b1=7.6

c.

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

Y Values
∑ = 36700
Mean = 6116.667
∑(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=0.979^2=0.958

d. Here

ŷ = 7.6X + 1746.7

For x=500, ŷ = (7.6*500) + 1746.7=5547