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We will start from an example, then to propose a demonstration of the general formulas on a simple case.

This article is addressed to the professors in particular, because it shows how the teaching of this topic can be carried out by the intermediary of the TI-89-92.

We will not detail the step, leaving with each one the care to equip it as it is appropriate to him.

Presentation on an example

We start from the principle which we do not know the method nor his results.

One considers a statistical series with 2 variables which corresponds to the following table:

X       2.1    1.8    3.4     5.1       6      7.2

y       6.9    4.7   10.8   13.8    16.2   14.1

One enters this table the computer by [ APPS ] Data/Matrix Editor.

One can then envisage the chart which corresponds to him. For that, one makes [ F2 ] then [ F1 ].

One then will ask the computer to determine the equation of the straight regression line without saying to the pupils that about which it all is.

One presses the key [ F5 ] and one enters the following options:

One then represents in the same reference mark the cloud and the curve.

The search of the equation of this curve is preceded by a presentation by the professor by the method of least squares.

Comes then a development step by step from the method.

Useful precision for the continuation : we called ACTIV the statistical table on TI-89-92.

One can easily make check that this curve passes by the average point of the cloud.

We will find the result starting from 2 statistical series with 4 unspecified elements (we took only 4 elements to facilitate the calculations carried out by the TI-89-92)

" general " case

One considers the 2 statistical series data by the following table:

X       a1   a2  a3  a4

y       b1   b2  b3  b4

One takes again the same step as précedemment.

The formula obtained can of multiple handling on the computer lead afterwards to a form " usable ". It is certainly preferable to make a written synthesis of it:

**time-out** B = - A/4 *aI - 1/4 *bI  (to i=1 to i=4) that one write more frequently under the form y_=a*x_+b, formula which highlight en évidence the membership of point average with straight regression line de régression.

The demonstration of A by the computer mainly poses some problems if one wants to obtain the usual formula, because of the immediate evaluations of partial results which prevent desired working. To block these evaluations, one must replace certain calculations by inert variables.

In the formula called sab, one will carry out following substitutions:

a1+a2+a3+a4 = sx1

a1+a2+a3+a4 = sx2

b1+b2+b3+b4 = sy1

b1+b2+b3+b4 = sy2

a1*b1+a2*b2+a3*b3+a4*b4 = sxy

One can carry out these replacements by successive handling on the computer, but it can be faster of réecrire the formula giving sab with the new variables.

B sécrit then B = - a*sx1/4 + sy1/4

The two formulas giving has and B being shown in the case of series to 4 elements, one can admit them for unspecified series. The demonstration was voluntarily built a little différement of that given in the particular case.

**time-out** we go return with this one to check that we find well the same result and thus put in obviousness that it be equivalent to begin of a way or of another.

Return to the particular case

Initially, it is necessary to supplement the table called ACTIV by a column giving the squares of variable X, and by a column giving the products of variables X and y.

The same results are found.

We can imagine other activities of the same kind to introduce and present other models of regression.

For our part, we will finish by the exposure of a a little unusual use to the level college (or BTS) of the quadratic or cubic regression.