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We get the, so-called, normal equations:
This is a system of linear equations with a and b as the unknowns, which can
be solved using the linear equation features of the calculator. There is,
however, no need to bother with these calculations because you can use the 3.
Fit Data … option in the ‚Ù menu as presented earlier.
Additional equations for linear regression
The summary statistics such as Σx, Σx
2
, etc., can be used to define the following
quantities:
Notes:
Θ a,b are unbiased estimators
of Α, Β.
Θ The Gauss-Markov theorem of probability indicates that among all
unbiased estimators for Α and Β, the least-square estimators (a,b) are the
most efficient.
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