- Average
- Linear model
- Quadratic polynomial model
- Exponential model
- Which model is the best one?
- Multiple variable model
- Nonlinear models
- Creating charts

The application Online multiple regression calculator let you achieve a regression analysis on your sample of data.

Let's have a look at the data drawn in the below graph.

If we would have only two points in the chart, then we would be able
to find an exact line *F(x) = a + bx* passing each point. If we would have
only three points in the chart, then we would be able to find an exact
parabola *F(x) = a + bx + cx ^{2}* passing each point. But we
have over 10 points and finding a polynom of such order would be
pointless.

We can find the average which is depicted below. It is
simple to determine average of all *f(x)*. It doesn't seem to be much helpful though:
the found solution doesn't fit the data well.

The data—with some degree of imperfection—are better represented by
a line *F(x) = a + bx*. Both coefficients a and b has to be determined.

Popular calculators CASIO
fx-991/fx-570
can find these coefficients:
press [MODE] 3 (STAT), [AC] and then enter the sample data pairs [*x*,
*y*]. Once finished, let's setup the regression analysis type to
linear: [SHIFT] 1 STAT 1 (Type) 2 (a + bx). Then let you display the computed coefficient: [AC] [SHIFT] 1 STAT 7 (Reg) 1 (a) to get value *a = -6.673*.
Similar way to get *b = 4.078*. So we got that *F(x) = -6.673 + 4.078 x*.
You can alter the input data if you press [SHIFT] 1 2 (Data). To leave the
regression mode: press [MODE] 1 (COMP).

And how does the description *F(x) = -6.673 + 4.078 x* looks like in the chart?

The CASIO calculator is useful but not that convenient and has its limits. The below online program is much more efficient.
Either you enter the data into the fields (RHS is right hand side or
simply *f(x)*) or you can directly paste the data into the textarea below
the cells. The two ticks select functions which have to be involved in
the analysis. In this case it is function *F _{1}(x) = 1* and

You likely expect to increase the degree of the function to the second
degree polynomial so it becomes *F(x) = a + bx + cx ^{2}*. You
still would have luck with the CASIO calculator but let's see how to use the
program. By default, there is no x

Eventually as a part of this excercise let's substitute *x ^{2}* guy by

There is no best model. The function *F(x)* has to consist of such
terms, which describe the analysed model well. Since models usually
some from the real world, there is known description but unknown
coefficients. The coefficients can be determined by the method of least
squares as the above used analyser does.

The parameter
MSE—which is being displayed as part of the results—tells us how
close the approximation *F(x)* is from the data being studied. It is a
parallel to standard deviation: the lower is the value, the better is
usually description. So if we look aside the physical meaning, the
exponential form fits the data better than the quadratic
form (MSE = 1.06 vs 1.24).

You can enter and solve multiple dimensions as well:

Either enter the data directly into the textfield or use the red handler right from the cells to stretch the table, so more columns are available for your input.

The current implementation doesn't support nonlinear least square method. It means that

- you are able to find coefficients
*a*and_{1}*a*if your model is_{2}

*F(x) = a*._{1}sin(x) + a_{2}e^{x} - But you won't be able to solve model if formed as

*F(x) = sin(a*._{1}x) + e^{a2 x}

The feature was considered but is not implemented in the current version. That might change in the future.

(c) 2016 Miroslav Stibor, back to the table of contents