Page 321 - Excel for Scientists and Engineers: Numerical Methods

298 EXCEL: NUMERICAL METHODS

( 13- 15)

( 13- 16)

R 2 =I- S‘resid (13-17)

“regression

F= SS r egression (13-18)

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The coefficient of determination, R2 (or the correlation coefficient, R), is a
measure of the goodness of fit of the data to (in this case) a straight line. If x and
y are perfectly correlated (Le., the difference between yobsd and ycalc is zero),
then R2 = 1. In contrast, an R2 value of zero means that there is no correlation
between x and y. A value of R2 of less than 0.9 corresponds to a rather poor fit of
data to a straight line.
The SEb) parameter, the standard error of the y estimate, is sometimes
referred to as the RMSD (‘oot-mean-square deviation).
The F-statistic is used to determine whether the proposed relationship is
significant (that is, whether y does in fact vary with respect to x). For most
relationships observed in chemistry, a relationship will unquestionably exist. If it
is necessary to determine whether the variation of y with x is statistically
significant, or merely occurs by chance, you can consult a book on statistics.

Linear Regression Using Trendline
You can also fit a least-squares line to data points such as those shown in
Figure 13-9 by adding a trendline to a chart. You can choose from a menu of
mathematical functions-linear, logarithmic, polynomial, power, exponential-
as curve-fitting functions.
To add a trendline, select the chart by clicking on it, then choose Add
Trendline.. . from the Chart menu.