HP 48gII Graphing Calculator Manuel d'utilisateur télécharger pdf (Page 621)

Suppose that we have n paired observations (x

); we predict y by means of

y = a + b⋅x, where a and b are constant.

Define the prediction error

The method of least squares requires us to choose a, b so as to minimize the

sum of squared errors (SSE)

bxayeSSE +−==

the conditions

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.

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• a,b are unbiased estimators

• 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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HP 48gII Graphing Calculator Manuel d'utilisateur Page 621