Answer:
Step-by-step explanation:
1-a See the attached photo for the a scattergraph.
1-b. Yes, the scattergraph show a near relationship between machine hours and power cost.
2. The power cost formula using the high and low points is as follows:
Total power cost = -7000 + (1.65 * Machine hours)
3-a. The power cost formula using the method of least squares is as follows:
Total power cost = 6454 + (1.21 * Machine hours)
3-b. R² = Coefficient of determination = 0.8969, or 89.69%
Explanation
1-a. Prepare a scattergraph by plotting power costs against machine hours.
Note: See the attached photo for the a scattergraph by plotting power costs against machine hours.
1-b. Does the scattergraph show a near relationship between machine hours and power cost?
Note that Scattergraph is interpreted by looking by looking for trends in the data as there is movement from left to right.
From the attached a scattergraph, it can be observed that there is an uphill pattern as there is a movement from left to right. This indicates that there a near positive relationship between power costs against machine hours.
Therefore, the scattergraph show a near relationship between machine hours and power cost.
2. Using the high and low points (i.e., the high-low method), compute a power cost formula.
2-a. Calculation of variable cost elements
Variable cost per machine hour = (Highest Power Costs - Lowest Power Costs) / (Highest machine hours – Lowest machine hours) = (42500 - 26000) / (30000 - 20000) = 1.65 per hour
2-b. Calculation of fixed cost elements
Total power cost = Total Fixed Cost + Total Variable Cost ................. (1)
Where;
Total Variable Cost = Variable cost per machine hour * Machine hours ……….. (2)
Substitute equation (2) into equation (1), we have:
Total power cost = Total Fixed Cost + (Variable cost per machine hour * Machine hours) ……………………. (3)
Using highest machine hours and substitute relevant values into equation (3), we have:
42500 = Total Fixed Cost + (1.65 * 3000)
42500 = Total Fixed Cost + 49,500
Total Fixed Cost = 42500 - 49,500
Total Fixed Cost = -7000
2-c Computation of a power cost formula
Substituting Variable cost per machine hour = 1.65 and Total Fixed Cost = -7000 into equation (3), we can compute the power cost formula as follows:
Total power cost = -7000 + (1.65 * Machine hours) ………………. (4)
Equation is the power cost formula.
3. Use the method of least squares to compute a power cost formula. Evaluate the coefficient of determination.
Note: See the attached excel file for the calculations of Total of Machine Hours (x), Power cost (y), xy, x^2, and y^2.
Since Σ = Total of or summation of, we can therefore obtain the following from the attached excel file:
Σx = 190,800
Σy = 282,500
Σxy = 6,878,400,000
Σx² = 4,666,540,000
Σy² = 10,188,250,000
N = Number of quarters = 8
3-a. Use the method of least squares to compute a power cost formula
Step 1: Calculation of variable cost per rental return
To calculate the variable power cost per machine hour, the following formula is used:
Variable power cost per machine hour = (NΣxy − ΣxΣy) /((NΣx²) − (Σx)²) ……………… (5)
= (Σxy – (1/8)ΣxΣy) /((Σx²) – (1/8)(Σx)²)
=(6,878,400,000 – ((1/8) * 190,800 * 282,500)) / (4,666,540,000 – ((1/8) * 190,800²))
Substituting the relevant values into equation (5), we have:
Variable cost per rental return = ((8 * 6,878,400,000) - (190,800 * 282,500)) /((8 * 4,666,540,000) - 190,800²)
Variable power cost per machine hour = 1.21
Step 2: Calculation of quarterly fixed power cost
This can be calculated using the following formula:
Fixed Cost per quarter = {Σy - (Variable power cost per machine hour * Σx) / N ....... (6)
Substituting the relevant values into equation (6), we have:
Fixed Cost per quarter = (282,500 - (1.21 * 190,800)) / 8
Fixed Cost per quarter = 6,454
Step 3: Computation of the power cost formula
Substituting Variable cost per machine hour = 1.21 and Total Fixed Cost = 6,454 into equation (3) in part 2 above, we can compute the power cost formula as follows:
Total power cost = 6454 + (1.21 * Machine hours) ………………. (4)
Equation (4) is the power cost formula.
3-b. Evaluate the coefficient of determination.
This can be evaluated using the following formula:
R² = Coefficient of determination = (NΣxy – ΣxΣy) / ((NΣx² - (Σx)²) * (NΣy² - (Σy)²))^0.5 ……….. (5)
Substituting the relevant values into equation (5) we have:
R² = ((8 * 6,878,400,000) – (190,800 * 282,500)) / (((8 * 4,666,540,000) – 190.800²) * ((8 * 10,188,250,000) – 282,500²))^0.5
R² = 0.8969, or 89.69%