Page 34 - 2017-v.2-Part 4(EN)

∑ xy − y ∑ x
b = (A.4)
∑ x −x ∑ x
2
Then a can be found by substitution:

a = y − bx (A.5)

2
For example, the following four values of x and y are noted during a test, from which ∑ ∑ x , x and
xy,
y are calculated as shown:

x y

No. (pedal force) (braking force)
N N
1 90 90
2 150 120

3 230 160
4 300 220

Sum ∑ x = 770 ∑ y = 590

Mean x = 192,5 y = 147,5

No. xy x 2
1 8 100 8 100
2 18 000 22 500
3 36 800 52 900
4 66 000 90 000

Sum ∑ xy = 128 900 ∑ xy = 173 500

∑ xy − y ∑ x
b =
∑ x − x ∑ x
2
128 900 − (147,5× 770)
=
173 500 −(192,5×770)
= 0,606

a = y − bx

= 147,5 – (0,606 × 192,5)

=30,8

The line of best fit is therefore

y = 30,8 + 0,60x

and the ±20 % limit lines are

80
y lower (30,8 + 0,606x )
=
100
= 24,64 + 0,485x

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