C sjc.cengagenow.com/ilrm/ta AssignmentMaindo?invoker=assignments&takeAssignment

Question

C sjc.cengagenow.com/ilrm/ta AssignmentMaindo?invoker=assignments&takeAssignmentSessionLocatoraassi-; d0 P 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) 400 450 550 600 700 750 Total Cost ($) 4000 5000 5400 5900 6400 7000 a. Compute bs and bo (to 2 decimals if necessary). bo Complete the estimated regression equation (to 2 decimals if necessary). b. What is the variable cost per unit produced (to 1 decimal)? c. Compute the coefficient of determination (to 4 decimals). Note: report between 0 and 1. What percentage of the variation in total cost can be explained by the production volume (to 2 decimals)7 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)? 628 PM 12/10/2017 Type here to search

Explanation / Answer

a.

calculation procedure for regression

mean of X = X / n = 575

mean of Y = Y / n = 5616.6667

(Xi - Mean)^2 = 93750

(Yi - Mean)^2 = 5648333.34

(Xi-Mean)*(Yi-Mean) = 712500

b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2

= 712500 / 93750

= 7.6

bo = Y / n - b1 * X / n

bo = 5616.6667 - 7.6*575 = 1246.67

value of regression equation is, Y = bo + b1 X

Y'=1246.67+7.6* X

b.

variable cost per unit is 7.6$

c.

calculation procedure for correlation

sum of (x) = x = 3450

sum of (y) = y = 33700

sum of (x^2)= x^2 = 2077500

sum of (y^2)= y^2 = 194930000

sum of (x*y)= x*y = 20090000

to caluclate value of r( x,y) = covariance ( x,y ) / sd (x) * sd (y)

covariance ( x,y ) = [ x*y - N *(x/N) * (y/N) ]/n-1

= 20090000 - [ 6 * (3450/6) * (33700/6) ]/6- 1

= 118750

and now to calculate r( x,y) = 118750/ (SQRT(1/6*20090000-(1/6*3450)^2) ) * ( SQRT(1/6*20090000-(1/6*33700)^2)

=118750 / (125*970.25)

=0.98

value of correlation is =0.98

coeffcient of determination = r^2 = 0.96

properties of correlation

1. If r = 1 Corrlation is called Perfect Positive Corrlelation

2. If r = -1 Correlation is called Perfect Negative Correlation

3. If r = 0 Correlation is called Zero Correlation

& with above we conclude that correlation ( r ) is = 0.9791> 0 ,perfect positive correlation

d.

production schedule shows 500 units then total cost estimated =

Y'=1246.67+7.6* X

Y' = 1246.67 +7.6*500

Y'=5046.67$

X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 400 4000 30625 2613611.22 282916.67 450 5000 15625 380277.82 77083.34 550 5400 625 46944.46 5416.67 600 5900 625 80277.76 7083.33 700 6400 15625 613611.06 97916.66 750 7000 30625 1913611.02 242083.33

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.