Your boss would like you to estimate the fixed and variable components of a particular cost. Actual data for this cost over four recent periods appear below. Using the least-squares regression method, what is the cost formula for this cost?
A) Y = $75.89 + $1.02X
B) Y = $72.64 + $2.13X
C) Y = $0.00 + $5.04X
D) Y = $75.50 + $2.02X

Question

Your boss would like you to estimate the fixed and variable components of a particular cost. Actual data for this cost over four recent periods appear below.  Using the least-squares regression method, what is the cost formula for this cost?
A) Y = $75.89 + $1.02X 
B) Y = $72.64 + $2.13X 
C) Y = $0.00 + $5.04X 
D) Y = $75.50 + $2.02X

Quizplus · Accepted Answer

Using the least-squares regression method, we can find the cost formula by calculating the slope and intercept of the line of best fit.

First, we need to calculate the variable cost per unit, which is the slope of the line. Using the formula for slope, we have:

slope = (nΣxy - ΣxΣy) / (nΣx^2 - (Σx)^2)

where n is the number of data points, Σxy is the sum of the products of each x and y value, Σx is the sum of the x values, Σy is the sum of the y values, and Σx^2 is the sum of the squared x values.

Plugging in the values from the table above, we get:

slope = (4(6443.5) - (42)(301.65)) / (4(386) - (42)^2) = 2.02

So the variable cost per unit is $2.02.

Next, we need to calculate the fixed cost, which is the y-intercept of the line. Using the formula for the y-intercept, we have:

y-intercept = ȳ - slope(x̄)

where ȳ is the average y value, x̄ is the average x value, and slope is the variable cost per unit that we just calculated.

Plugging in the values from the table above, we get:

ȳ = (301.65 + 487.35 + 718.80 + 907.20) / 4 = 376.75
x̄ = (10 + 15 + 20 + 25) / 4 = 17.5

y-intercept = 376.75 - 2.02(17.5) = 75.50

So the fixed cost is $75.50.

Putting it all together, the cost formula is:

Y = $75.50 + $2.02X

Therefore, the best choice is D, Y = $75.50 + $2.02X.

Your Boss Would Like You to Estimate the Fixed and Variable