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 4,700 450 5,700 550 6,100 600 6,600 700 7,100 750 7,700 Compute b1 and b0 (to 1 decimal). b1 b0 Complete the estimated regression equation (to 1 decimal). = + x What is the variable cost per unit produced (to 1 decimal)? 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)? % 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)

(i)

From the given data, the following statistics are calculated:

X	Y	XY	X2	Y2
400	4700	1880000	160000	22090000
450	5700	2565000	202500	32490000
550	6100	3355000	302500	37210000
600	6600	3960000	360000	43560000
700	7100	4970000	490000	50410000
750	7700	5775000	562500	59290000
Total = 3450	37900	22505000	2077500	245050000

Slope b₁ is given by:

y - Intercept b₀ is given by:

So,

Answer is:

b₁ = 7.6

b₀ = 1946.7

(ii)

The Estimated Regression Equation is given by:

(b)

Variable cost per unit produced = 7.60

(c)

Correlation Coefficient (r) is got as follows:

Coefficient of Determination (R²) is given by:

R² = 0.9791² = 0.959

(d)

The percentage of the variation in total cost can be explained by the production volume = 95.9 %

(e)
For x = 500, we get:

So,

Answer is:

5747