The following 6 months of data were collected on electricity cost and the number of machine hours in a factory.

- A dependent variable value used in calculating the cost line using the high-low method is:
A) $27,900
B) 5,430
C) $25,160
D) 4,500

Question

The following 6 months of data were collected on electricity cost and the number of machine hours in a factory.

- A dependent variable value used in calculating the cost line using the high-low method is:
A) $27,900 
B) 5,430 
C) $25,160 
D) 4,500

Quizplus · Accepted Answer

The high-low method involves selecting the highest and lowest levels of the independent variable (in this case, machine hours) and using the corresponding costs to calculate the cost line. From the data provided, the highest level of machine hours is 8,760 and the corresponding cost is $27,900. The lowest level of machine hours is 1,800 and the corresponding cost is $5,430. Using these numbers, we can calculate the slope of the cost line as (27,900 - 5,430) / (8,760 - 1,800) = $2.69 per machine hour. To find the y-intercept (i.e. the fixed cost), we can use either of the two data points and the slope:

y - 5,430 = 2.69(x - 1,800)
y - 5,430 = 2.69x - 4,842
y = 2.69x + 588

Plugging in the numbers from the data point (8,760, 27,900):

27,900 = 2.69(8,760) + b
b = 3,758.40

Therefore, the cost line equation is: y = 2.69x + 3,758.40. Using this equation, we can calculate the cost for any level of machine hours. However, the question specifically asks for a dependent variable value used in calculating the cost line. The only answer choice that fits this description is option C, which corresponds to the cost at the low level of machine hours used in the calculation of the slope and y-intercept.

The Following 6 Months of Data Were Collected on Electricity