Question

Albedo Inc. manufactures high-end replacement telescope lenses for amateur and professional astronomers who are seeking to upgrade the performance of their telescopes. You have just become employed as a staff accountant at Albedo, and Jordan Coleman, the controller, has asked you to help with maintenance cost estimation for the lens manufacturing process. You review the manufacturing process and decide that the best cost driver for maintenance costs is machine hours. The data below are from the previous fiscal year for maintenance costs and machine hours:

Month	Maintenance Cost			Machine Hours
1	$	3,210		2,750
2		4,650		3,900
3		5,175		4,050
4		3,350		2,690
5		3,100		2,500
6		2,950		2,580
7		2,900		2,300
8		2,900		2,500
9		4,120		3,160
10		4,350		3,325
11		3,500		2,780
12		3,775		3,000

Required:

1. What is the cost equation for maintenance costs using the high-low method? (Round "slope (unit variable cost)" to 2 decimal places. Negative amounts should be indicated by a minus sign.)

2. Graph the data and comment on whether or not there are potential outliers. (To earn full credit for this graph you must plot all required points for each curve. While plotting the points a tool icon will pop up. You can use this to enter exact co-ordinates for your points as needed.)

2. Graph the data and comment on whether or not there are potential outliers. (To earn full credit for this graph you must plot all required points for each curve. While plotting the points a tool icon will pop up. You can use this to enter exact co-ordinates for your points as needed.)

Answer 1

When months 3 and 7 are used for the high and low points respectively, the high-low method provides the following cost equation: Cost = $-90 + $1.30 × hours.

The graph below shows that the data are very nearly linear; there are no outliers.

Month 1 2 3 4 5 6 7 8 9 10 11 12 Maintenance Machine Costs Hours 2750 3210 3900 4650 4050 5175 High 2690 3350 2500 3100 2580 2950 2300 2900 Low 2500 2900 3160 4120 3325 4350 2780 3500 3000 3775

Slope (b) = 1.30 =(5175-2900) ÷ (4050-2300)
Constant (a) = -90 =5175 - 1.30 x 4050
Cost equation = $-90 + $1.30 × Hours

6000 5000 4000 Costs 3000 2000 1000 0 0 1000 2000 3000 4000 5000 Hours

The constant term in the solution is a negative number. This is a good opportunity to explain to the students that a negative intercept term can arise in a high-low or a regression solution. The reason why is that the relevant range for the independent variable is too far from the intercept, so that the best-fitting high-low line or regression line may have a negative intercept. Chapter 3 included a discussion of the relevant range, with the instruction that predictions of total cost should be limited to levels of the independent variable that fall within the relevant range. This would be a good time to remind the students of the concept of the relevant range and how it applies to cost estimation.

This also reminds us that the value of a, the intercept, should not be generally interpreted as fixed cost, especially when the relevant range of the independent variable is far from the origin. The value of a is very useful in developing the predicted cost from the cost estimation equation but cannot be used to infer the level of fixed cost. Note that the text defines a as “a fixed quantity that represents the value of Y when X is zero.” The illustration below shows the high-low line extended to the origin and the negative intercept; the data below 2,300 hours is outside the relevant range.

Predicted Cost 6,000 5,000 4,000 3,000 -Predicted Cost 2,000 1,000 (1,000) (1,000) 1,000 2,000 3,000 4,000 5,000