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 4100 500 4600 550 5600 650 6400 700 6800 750 7200 The data on the production volume $x$ and total cost $y$ for particular manufacturing operation were used to develop the estimated regression equation $y = 285.65 + 9.29x$. a. The company's production schedule shows that 450 units must be produced next month. What is the point estimate of the total cost for next month? $\hat{y} = 4466.1$ (to 2 decimals) b. Develop a 95% prediction interval for the total cost for next month. $ \text{ } $ (to 2 decimals) $t\text{-value}$ (to 3 decimals) $s_{pred}$ (to 2 decimals) Prediction Interval for an Individual Value: ( , ) (to whole number)
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First, we need to find the regression equation. We can use the least squares method to find the slope (b1) and the intercept (b0) of the regression line. Show more…
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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 3,500 450 4,500 550 4,900 600 5,400 700 5,900 750 6,500 a. Compute b1 and b0 (to 1 decimal). b1 b0 Complete the estimated regression equation (to 1 decimal). y = [ ] + [ ]x b. What is the variable cost per unit produced (to 1 decimal)? c. Compute the coefficient of determination (to 3 decimals). Note: report r^2 between 0 and 1. r^2 = 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)? $
Jerelyn N.
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 5,000 450 6,000 550 6,400 600 6,900 700 7,400 750 8,000 a. Compute b1 and b0 (to 1 decimal). b1 7.6 b0 1247 Complete the estimated regression equation (to 1 decimal). y = 1247 + 7.6x b. What is the variable cost per unit produced (to 1 decimal)? $ 7.6 c. Compute the coefficient of determination (to 3 decimals). Note: report r^2 between 0 and 1. r^2 = 0.959 What percentage of the variation in total cost can be explained by the production volume (to 1 decimal)? 96 % 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)? $ 5047
Sri K.
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 4,100 450 5,100 550 5,500 600 6,000 700 6,500 750 7,100 a. Compute b1 and b0 (to 1 decimal). b1 = b0 = Complete the estimated regression equation (to 1 decimal). y = + x b. What is the variable cost per unit produced (to 1 decimal)? c. Compute the coefficient of determination (to 3 decimals). Note: report r^2 between 0 and 1. r^2 = 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)? $
Adi S.
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