Hp 50g Graphing Calculator Uživatelský manuál stáhnout pdf (Strana 630)

100

101

Page 18-63

Θ The correlation coefficient, r. This value is constrained to the range –1

< r < 1. The closer r is to +1 or –1, the better the data fitting.

Θ The sum of squared errors, SSE. This is the quantity that is to be

minimized by least-square approach.

Θ A plot of residuals. This is a plot of the error corresponding to each of

the original data points. If these errors are completely random, the

residuals plot should show no particular trend.

Before attempting to program these criteria, we present some definitions

Given the vectors x and y of data to be fit to the polynomial equation, we form

the matrix X and use it to calculate a vector of polynomial coefficients b. We

can calculate a vector of fitted data, y’, by using y’ = X⋅b.

An error vector is calculated by e = y – y’.

The sum of square errors is equal to the square of the magnitude of the error

vector, i.e., SSE = |e|

= e•e = Σ e

= Σ (y

-y’

)

To calculate the correlation coefficient we need to calculate first what is known

as the sum of squared totals, SST, defined as SST = Σ (y

-⎯y)

, where ⎯y is the

mean value of the original y values, i.e., ⎯y = (Σy

)/n.

In terms of SSE and SST, the correlation coefficient is defined by

r = [1-(SSE/SST)]

1/2

Here is the new program including calculation of SSE and r (Once more,

consult the last page of this chapter to see how to produce the variable and

command names in the program):

« Open program

 x y p Enter lists x and y, and number p

« Open subprogram1

x SIZE  n Determine size of x list

« Open subprogram 2

1 2 ... 625 626 627 628 629 630 631 632 633 634 635 ... 886 887

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