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.

Production Volume (units) Total Cost ($) 400 4,200 450 5,200 550 5,600 600 6,100 700 6,600 750 7,200

Compute b1 and b0 (to 1 decimal). b1 b0

Complete the estimated regression equation (to 1 decimal). = + x

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

Compute the coefficient of determination (to 3 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 1 decimal)? %

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)? $

Explanation / Answer

The Regression equation is

y=a+bx

From Excel

a)b1 =7.6

b0=1446.7

b)) The fitted regressionn equation is'

y= 1446.7 + 7.6(units)

c) variable cost per unit produced is 7.6

d) coefficient of determination is 0.96

96% of variation in total cost can be explained by the production volume

e) when x=500

y=1446.7 +7.6(units)

y=1446.7+7.6*500

y=5246.7

SUMMARY OUTPUT Regression Statistics Multiple R 0.979127 R Square 0.95869 Adjusted R Square 0.948362 Standard Error 241.5229 Observations 6 ANOVA df SS MS F Significance F Regression 1 5415000 5415000 92.82857 0.000649 Residual 4 233333.3 58333.33 Total 5 5648333 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 1446.667 464.1599 3.116742 0.035639 157.9521 2735.381 157.9521 2735.381 units 7.6 0.788811 9.634759 0.000649 5.409911 9.790089 5.409911 9.790089

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