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.

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)?
$

Production Volume (units) Total Cost ($) 400 5,000 450 6,000 550 6,400 600 6,900 700 7,400 750 8,000

Explanation / Answer

sol:

totalcost=2246.667+7.6(productionvolume)

Complete the estimated regression equation (to 1 decimal).

totalcost=2246.7+7.6(production volume)

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

slope=y/x=cost/unit

Compute the coefficient of determination (to 3 decimals). Note: report r2 between 0 and 1.
r2 =  

r2=0.959

What percentage of the variation in total cost can be explained by the production volume (to 1 decimal)?

=0.959*100=95.9%

e estimated total cost for this operation (

=2246.7+7.6(production volume)

=2246.7+7.6(500)

=6046.7

=6047

answer:6047

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% Intercept 2246.667 464.1599 4.840286 0.008398 957.9521 3535.381 Production Volume (units) 7.6 0.788811 9.634759 0.000649 5.409911 9.790089

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