Question

21. 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 produc- tion 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. 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.

Answer 1

Answer:-

Caluilate Regrettim ean by wning Least squexe 282916.661 calculations methed. Production folume total cost cy) X-KY (x-7) ² - 72 (X-X)/4-9) 400 4000 -145-1616.669 30625 | 2613611.1) 450 Soro -125 -616.667 15625 | 380217:33 ng 083-33 550 5400 -25 216.667 .625 | 46944144 5416,667 600 5900 25 283,333 625 80207.78 7083-33 100 6450 125 783.333 156254 613611.11 99 916.667 750 7000 175 1383,333 30625 1913611-1) 242083.33 3450 33700 939501 5648333. 34 7125001 do 5:15 5616667 total mean a) y = a +bx 20 is simple Requession egn b=slope = { CX-) (yng) - 412500 7.6 EX~%) 2 930450 qe intercepto y - bx = 5616.64-(746X545) = 1246166669 :: Estimated Regseggian equation is 23 1246.66667 + 406 x b) rociable cost pe unit peaduced $ 9.6 Coefficient of determination, ²= (correlation) ro correlation bets production volume of total cost Ecx-* cyný). Eix])28f4-772 93950X 5648993733 0.9791 0.9586 & 95.86 % of the relation in total cost.com be explained by production production bolumes 2 12900 g2=

Page two

4 ) if production cost is soo Cie x=500) then from eario, go o 1246.60667 +7.6 X500 5046.66689 peedicted total cost for this $ 5046.66667

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