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TBIS 79010:2019
Annex A
(Informative)
Explanation of the method of least squares for obtaining line of best
fitand ± 20 % limit lines for braking performance linearity
The readings taken in the test specified in 4.2.2.9.3.6 can be expected to lie near
some straight line that can be drawn through them. Although in practice one might
draw a good straight line through the points by eye, the method of least squares
given here provides a criterion for minimising the discrepancies, and permits a line to
be selected that has a claim to be called the best fit.
The line of best fit is the line that minimises the sum of the squares of the
differences between the observed results and the corresponding results predicted by
the line.
The relationship between the variables is considered to be of the form:
y = a + bx
Where
x is the independent variable, and is known precisely (in this case the load applied to the pedal);
y is the dependent variable, and is observed but with a degree of uncertainty (in this case, the
braking force at the wheel);
a and b are unknown constants and have to be estimated.
For a series of n readings, this relationship can be resolved by taking a minimum of
the sum of the squares of the difference to give:
Taking:
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