ACCA MA · Chapter 2 · Question 6 of 12
A company has the following data for five periods, where x is output (000 units) and y is total cost ($000): Sum of x = 50, Sum of y = 400, Sum of xy = 4,300, Sum of x squared = 540, n = 5 Using linear regression (y = a + bx), what is the estimated total cost ($000) when output is 12,000 units?
Test yourself: pick an answer
Reveal answer & explanation
Correct answer: A) 95.0
Explanation
b = (n x sum xy - sum x x sum y) / (n x sum x squared - (sum x) squared) = (5 x 4,300 - 50 x 400) / (5 x 540 - 50 x 50) = (21,500 - 20,000) / (2,700 - 2,500) = 1,500 / 200 = 7.5. a = (sum y - b x sum x) / n = (400 - 7.5 x 50) / 5 = 25 / 5 = 5. At x = 12: y = 5 + 7.5 x 12 = 95.0, i.e. $95,000.
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