ACCA PM · Chapter 11 · Question 7 of 10
A company uses linear regression (y = a + bx) to estimate overhead costs (y, $000) from machine hours (x, 000 hours). From five observations: n = 5, sum of x = 50, sum of y = 500, sum of xy = 5,240 and sum of x squared = 540. Using b = (n sum xy - sum x sum y) / (n sum x^2 - (sum x)^2) and a = (sum y / n) - b(sum x / n), what is the forecast overhead cost when 15,000 machine hours are worked?
Test yourself: pick an answer
Reveal answer & explanation
Correct answer: B) $130,000
Explanation
b = (5 x 5,240 - 50 x 500) / (5 x 540 - 50^2) = (26,200 - 25,000) / (2,700 - 2,500) = 1,200 / 200 = 6. a = (500 / 5) - 6 x (50 / 5) = 100 - 60 = 40. Forecast y = 40 + (6 x 15) = 130, so overheads are $130,000.
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