A. Compute b 1 and b 0 (to 2 decimals if necessary). b 1 : (BLANK) b 0 : (BLANK)

Question

A. Compute b1 and b0 (to 2 decimals if necessary).
b1 : (BLANK)
b0 : (BLANK)

Complete the estimated regression equation (to 2 decimals if necessary).
y = (BLANK) + (BLANK)  x

B. What is the variable cost per unit produced (to 1 decimal)?
$ (BLANK)

C. Compute the coefficient of determination (to 4 decimals). Note: report r^2 between 0 and 1.
r^2 = (BLANK)

What percentage of the variation in total cost can be explained by the production volume (to 2 decimals)?
(BLANK) %

D. The company's production schedule shows 500 units must be produced next month. What is the estimated total cost for this operation (to 2 decimals)?
$ (BLANK)

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 4000 450 5000 550 5400 600 5900 700 6400 750 7000

A. Compute b1 and b0 (to 2 decimals if necessary).
b1 : (BLANK)
b0 : (BLANK)

Complete the estimated regression equation (to 2 decimals if necessary).
y = (BLANK) + (BLANK)  x

B. What is the variable cost per unit produced (to 1 decimal)?
$ (BLANK)

C. Compute the coefficient of determination (to 4 decimals). Note: report r^2 between 0 and 1.
r^2 = (BLANK)

What percentage of the variation in total cost can be explained by the production volume (to 2 decimals)?
(BLANK) %

D. The company's production schedule shows 500 units must be produced next month. What is the estimated total cost for this operation (to 2 decimals)?
$ (BLANK)

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Total Cost ($)
Independent Variable: Production Volume (units)
Total Cost ($) = 1246.6667 + 7.6 Production Volume (units)
Sample size: 6
R (correlation coefficient) = 0.9791271
R-sq = 0.95868988
Estimate of error standard deviation: 241.52295

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

A) b1 = 7.60

b0 = 1246.67

B) Variable cost per unit = Slope = 7.6

C) r^2 = 0.9587

Percentage of variation explained = 95.87%

D) Estimated total cost = $ 5046.67

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 1246.6667 464.15993 0 4 2.6858558 0.0549 Slope 7.6 0.78881064 0 4 9.6347585 0.0006

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