An important application of regression analysis in accounting is in the estimati

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.

a. Compute b1 and b0 (to 2 decimals if necessary).
b1  
b0  

Complete the estimated regression equation (to 2 decimals if necessary).
y = _ + _  x

b. What is the variable cost per unit produced (to 1 decimal)?
$

c. Compute the coefficient of determination (to 4 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 2 decimals)?
%

d. The company's production schedule shows 500 units must be produced next month. What is the estimated total cost for this operation (to 2 decimals)?
$

Production Volume (units) Total Cost ($) 400 4000 450 5000 550 5400 600 5900 700 6400 750 7000

Explanation / Answer

Here lets say regresion line is

y^ = b0 + b1 x

Here y^ = predicted Total cost

x = productio volume.

so we will calculate regression coefficient by x,y,xy, x2

Here the table for these values

Here b0 = [(y) (x2 ) - (x) (xy)]/ [ n (x2 ) - (x)2 ]

b0 = [33700 * 2077500 - 3450 * 20090000] / [ 6 * 2077500 - 34502]

b0 = 701250000/ 562500 = 1246.67

b1 =  [ n(xy) - (x)((y)]/ [ n (x2 ) - (x)2 ]

b1 = [ 6 * 20090000 - 3450 * 33700] / [6 * 2077500 - 34502]

b1 = 4275000/ 562500 = 7.6

y^ = 7.6x + 1246.67

(b) Variable cost per unit = $7.6

(c) Coefficient of determination

R2 = [n(xy) - (x)((y)]2 / [ (n (x2 ) - (x)2) ( n (y2 ) - (y)2]

R2 = [ 6 * 20090000 - 3450 * 33700]2 / [(6 * 2077500 - 34502 ) * (6 * 194930000 - 337002]

R2 = 18275625000000/ (562500 * 33890000)

R2 = 0.9587

What percentage of the variation in total cost can be explained by the production volume?

= 95.87%

(d) d. The company's production schedule shows 500 units must be produced next month. What is the estimated total cost for this operation

Estimated total cost = 1246.67 + 7.6 * 500 = $ 5046.67

Production Volume (units) (x) Total Cost ($)(y) x^2 xy y^2 400 4000 160000 1600000 16000000 450 5000 202500 2250000 25000000 550 5400 302500 2970000 29160000 600 5900 360000 3540000 34810000 700 6400 490000 4480000 40960000 750 7000 562500 5250000 49000000 Sum 3450 33700 2077500 20090000 194930000

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