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	5,000
450	6,000
550	6,400
600	6,900
700	7,400
750	8,000

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

(a)

From the given data, the following table is calculated:

X	Y	XY	X2
400	5000	2000000	160000
450	6000	2700000	202500
550	6400	3520000	302500
600	6900	4140000	360000
700	7400	5180000	490000
750	8000	6000000	562500
Total = 3450	39700	23540000	2077500

Slope b1 is given by:

Intercept b0 is given by:

Estimated Regression Equation is given by:

(b)

The variable cost per unit produced = 7.6

(c)

From the given data, the following table is calculated:

X	Y	XY	X2	Y2
400	5000	2000000	160000	25000000
450	6000	2700000	202500	36000000
550	6400	3520000	302500	40960000
600	6900	4140000	360000	47610000
700	7400	5180000	490000	54760000
750	8000	6000000	562500	64000000
Total = 3450	39700	23540000	2077500	268330000

The Correlation Coefficient (r) is given by:

Coefficient of Determination = R² = 0.9791² = 0.959

Percentage of variation explained = 95.9 %

(d)
For x = 500, we get:

So,

Answer is:

6047