Page 262 - F2 - MA Integrated Workbook STUDENT 2018-19

Chapter 12

Example 1

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

x y x 2 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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