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Thane Company is interested in establishing the relationship between electricity costs and machine hours. Data have been collected and a regression analysis prepared using Excel. The monthly data and the regression output follow:
Month Machine Hours Electricity Costs
January 2,900 $ 18,600
February 3,300 $ 21,400
March 2,300 $ 13,700
April 3,500 $ 23,400
May 4,200 $ 28,450
June 3,700 $ 22,400
July 4,500 $ 24,950
August 3,900 $ 22,950
September 2,400 $ 15,900
October 4,100 $ 26,400
November 5,300 $ 31,400
December 4,900 $ 27,950
Summary Output
Regression Statistics
Multiple R .959
R Square .920
Adjusted R2 .912
Standard Error 1,550.32
Observations 12.00
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 2,992.80 1,933.78 1.55 0.15 (1,315.92) 7,301.52
Machine Hour 5.37 0.50 10.70 0.00 4.25 6.49
If the controller uses the high-low method to estimate costs, the cost equation for electricity cost is: (Round intermediate calculations to 2 decimal places.)
A. Cost = $2,992.80 + $5.37 × Machine-hours.
B. Cost = $130.00 + $5.90 × Machine-hours.
C. Cost = $6.50 × Machine-hours.
D. Cost = $23,670.

Respuesta :

Answer:

The correct option : B. Cost = $ 130.00 + $ 5.90 x Machine - hours

Explanation:

Let's use the following method to solve the given problem

Now applying the high-low method of cost estimation,

High => November, 5,300 machine hours

Low => March, 2,300 machine hours

Arranging it in a simultaneous equations for total cost:

We can let fixed cost per month to be F, and the variable cost per machine -hour be V, and the number of machine-hours be Q.

Therefore

Total cost = F + VQ

High => F + 5,300Q = $ 31,400

Low => F + 2,300Q = $ 13,700

Subtracting Low from High, we have 3,000Q = $ 17,700 or Q = $ 5.90 per machine hour ................equation one

F = $ 13,700 - ( 2,300 x $ 5.90) = $ 130......................................................................equation two