question archive Jim Beaumont, the owner of Lube ‘n’ Go, is interested in determining the fixed and variable costs of performing a standard oil change
Jim Beaumont, the owner of Lube ‘n’ Go, is interested in determining the fixed and variable costs of performing a standard oil change
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Jim Beaumont, the owner of Lube ‘n’ Go, is interested in determining the fixed and variable costs of performing a standard oil change. Since the oil changes are fairly standard, each one taking about the same amount of time and using about the same amount of grease, paper towels, etc., Jim thinks the number of oil changes would be a good independent variable. The total monthly cost includes the salaries of the two service persons, depreciation on the facility and equipment, utilities, and supplies such as grease and wipes. (The cost of oil is not included, as it differs from car to car and is charged to each customer based on the number of quarts actually used.) Data for the past eight months are as follows:
Month Number of Oil Changes Total Cost
|
May |
1,100 |
$7,150 |
|
June |
1,400 |
7,950 |
|
July |
1,380 |
8,350 |
|
August |
1,250 |
7,425 |
|
September |
890 |
5,730 |
|
October |
900 |
5,730 |
|
November |
850 |
5,450 |
|
December |
700 |
5,150 |
Required
1. Prepare a scattergraph based on these data. Use cost for the vertical axis and number of oil changes for the horizontal. Based on an examination of the scat- tergraph, does there appear to be a linear relationship between the cost of oil changes and the number of oil changes performed?
2. Compute the cost formula for oil changing services using the high-low method. Calculate the predicted cost for January for 1,000 oil changes using the high-low formula.
3. Compute the cost formula for oil change services using the method of least squares. Using the regression cost formula, what is the predicted cost for January for 1,000 oil changes? What does the coefficient of determination tell you about the cost formula computed by regression?
4. Which cost formula—the one computed using the high-low method or the one using the least-squares coefficients—do you think is better? Explain.
