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 4,000 450 5,000 550 5,400 5,900 700 6,400 750 7,000 a. Compute bi and bo (to 1 decimal). b1 600 Complete the estimated regression equation (to 1 decimal). ĝ= b. What is the variable cost per unit produced (to 1 decimal)? c. Compute the coefficient of determination (to 3 decimals). Note: report p2 between 0 and 1. What percentage of the variation in total cost can be explained by the production volume (to 1 decimal)? d. 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

400 450| 550 1600 1700 750 4000 160000 16000000| 5000| 202500| 25000000 5400 302500| 29160000|| 5900| 360000 34810000 6400 490000 40960000|| 7000 562500| 49000000 1600000 2250000 2970000 3540000 4480000, 5250000 | 3450|| 33700| 2077500| 194930000| 20090000,

x = 3450 2y = 33700 2xy = 20090000 {x} = 2077500 [y= 194930000 n= 6 2077500 -3450-16 = 93750 194930000 -33700216 = 5648333.33 20090000-(3450*33700)/6 = 712500.00 a) Sxx = {x?- (Ex)²/n = Syy = [y?- (Ey)? = Sxy = {xy- (Ex*Zy/n = Regression equation ŷ = bo + bịx Slope bı = Sexy Intercept bo = 2y - b, Ex = Regression equation ĝ= 1246.7+7.6x 712500 /5648333.33 7.6 (33700/6)-7.6*(3450/6) = 1246.7 n

Regression equation ŷ=bo +b x = Slope bį = Sxy Intercept bo = 29 - b, 2x = 712500 /5648333.33 (33700/6)-7.6*(3450/6)= 7.6 1246.7 поп Regression equation ŷ= 1246.7+7.6x Variable cost per unit produced is $7.6 increased Sxyz Correlation coefficient r=- SxxSyy =712500 /\(93750*5648333.33) 0.979 coeficient of determiantion r? = 0.959 Explained variation 95.9% Given x = 500 units Pridicetd value y^=1246.7+7.6*500 5046.7