User`s guide

3 Fitting Data
3-30
For the current fit, these statistics are displayed in the Results list box in the
Fit Editor. For all fits in the current curve-fitting session, you can compare the
goodness of fit statistics in the
Table of fits.
Sum of Squares Due to Error. This statistic measures the total deviation of the
response values from the fit to the response values. It is also called the summed
square of residuals and is usually labeled as SSE.
A value closer to 0 indicates a better fit. Note that the SSE was previously
defined in “The Least Squares Fitting Method” on page 3-6.
R-Square. This statistic measures how successful the fit is in explaining the
variation of the data. Put another way, R-square is the square of the correlation
between the response values and the predicted response values. It is also called
the square of the multiple correlation coefficient and the coefficient of multiple
determination.
R-square is defined as the ratio of the sum of squares of the regression (SSR)
and the total sum of squares (SST). SSR is defined as
SST is also called the sum of squares about the mean, and is defined as
where SST = SSR + SSE. Given these definitions, R-square is expressed as
R-square can take on any value between 0 and 1, with a value closer to 1
indicating a better fit. For example, an R
2
value of 0.8234 means that the fit
explains 82.34% of the total variation in the data about the average.
SSE
w
i
y
i
y
ˆ
i
–()
2
i 1=
n
∑
=
SSR
w
i
y
ˆ
i
y–()
2
i 1=
n
∑
=
SST
w
i
y
i
y–()
2
i 1=
n
∑
=
R-square
SSR
SST
------------- 1=
SSE
SST
-------------–=