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Statistical techniques

3.2 Using liner regression

Using the following data we will calculate a (the fixed cost) and b (the
variable cost). The numbers in the calculations can get big so the
figures are shown in 000s.
Activity level Cost

2
x y x xy
Quarter 1 10 38.3 100 383

Quarter 2 12 42.7 144 512.4
Quarter 3 9 35.7 81 321.3

Quarter 4 14 47.2 196 660.8
–––– –––– –––– ––––––

45 163.9 521 1,877.5
–––– –––– –––– ––––––

n∑xy – ∑x∑y (4 × 1,877.5) – (45 × 163.9) 134.5

b = ——————— = ———————————— = ——— = 2.28
2
2
n∑x – (∑x) (4 × 521) − 45 2 59
a = y ̅ − b x ̅ = (163.9 ÷ 4) − 2.28 × (45 ÷ 4) = 15.325

Regression uses all of the observations rather than just the highest and lowest so
gives a better estimation of a and b.

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