An important application of regression anaylsis in accounting is in the estimati
ID: 3334854 • Letter: A
Question
An important application of regression anaylsis 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 400 450 550 600 700 750
Total Cost 4000 5000 5400 5900 6400 7000
a. use these data to develop an estimated regression equation that could be used to predict the total cost for a given production volume.
b. what is the variable cost per unit produced?
c. Compute the coefficient of determination. What percentage of the variation in total cost can be explained by production volume?
d. The company's production schedule shows 500 units must be produced next month. Predict the total cost for this operation.
Explanation / Answer
a)
Total Cost (y)
Production Volume (x)
x^2
y^2
xy
4000
400
160000
16000000
1600000
5000
450
202500
25000000
2250000
5400
550
302500
29160000
2970000
5900
600
360000
34810000
3540000
6400
700
490000
40960000
4480000
7000
750
562500
49000000
5250000
33700
3450
2077500
194930000
20090000
r (correlation)=n(Exy)-(Ex)(Ey)/sqrt(nEx2-(Ex)2)(nEy2-(Ey)2)
=6(20090000)-(3450)(33700)/(6*2077500-(3450)^2)(6*194930000-(33700)^2)
=0.9791
r^2=0.9587
b1=nE(xy)-ExEy/nE(x2)-(Ex2)
=6(20090000)-(3450)(33700)/6*2077500-(3450)^2
=7.6
b0=Ey-b1Ex/n
=33700-(7.6)(3450)/6
=1246.67
b)
7.6
c)
r^2=0.9587 which means 95.87% of variation in dependent variable is accounted for by the independent variable.
d)
y=1246.67+7.6x
y=1246.67+7.6(500)
y=5046.67
Excel Output: -
Total Cost (y)
Production Volume (x)
x^2
y^2
xy
4000
400
160000
16000000
1600000
5000
450
202500
25000000
2250000
5400
550
302500
29160000
2970000
5900
600
360000
34810000
3540000
6400
700
490000
40960000
4480000
7000
750
562500
49000000
5250000
33700
3450
2077500
194930000
20090000
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