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 3,900 450 5,100 550 5,400 600 5,900 700 6,400 750 7,100 (a) Use these data to develop an estimated regression equation that could be used to predict the total cost for a given production volume. (Round your numerical values to two decimal places.) ý = (b) What is the variable cost (in dollars) per unit produced? $ (c) Compute the coefficient of determination. (Round your answer to three decimal places.) What percentage of the variation in total cost can be explained by production volume? (Round your answer to one decimal place.) % (d) The company's production schedule shows 500 units must be produced next month. Predict the total cost in dollars) for this operation. (Round your answer to the nearest cent.) $

Answer 1

The statistical software output for this problem is :

Simple linear regression results: Dependent Variable: y Independent Variable: x y=1125.3333 + 7.84x Sample size: 6 R (correlation coefficient) -0.96771279 R-sq=0.93646804 Estimate of error standard deviation: 312.62331 Parameter estimates: Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 1125.3333 600.80095 #0 4 1.8730552 0.1344 Slope 7.84 1.0210235 +04 7.67857 0.0015 Analysis of variance table for regression model: Source DF SS MS F-stat P-value Model 1 5762400 5762400 58.960437 0.0015 Error 4 390933.33 97733.333 Total 5 6153333.3 Predicted values: X value Pred. Y s.e.(Pred. y) 95% C.I. for mean 95% P.I. for new 500 5045.3333 148.83847 (4632.0915,5458.5752) (4084.0006, 6006.666)

(a)

$\hat y$ = 1125.33 + 7.84 x

(b)

Variable cost = $ 7.84

(c)

r ² = 0.936

93.6%

(d)

$ 5045.33