Predicting using the PLOT view
RelErr as a measure of non-linear fit
Using the
PLOT
view is the probably the more visually appealing
method of obtaining predicted values. When you have plotted a set of
data and its fit curve then pressing up arrow will change the focus of the
values at the bottom of the screen from the data points to the
PREDY
values. In the screen snapshots shown right the focus changes from data
point
3:(2,2)
, to the
PREDY
value for x = 2 of 2.806.
If there is more than one data set (and fit lines) graphed then the up
arrow will move progressively from one to another and finally back to
the first.
Pressing left and right arrows will move along the fit line but only on pixel positions, which may not be
suitable if the scale is not chosen carefully. A better way is to use the
key to obtain
PREDY
values for
any required value of
x
, including values which would normally be off-screen.
coefficient quoted in the
Mathematically,
Another aspect of bivariate stats needs to be remembered when the fit chosen is not linear.
the correlation coefficient is a strictly linear measure of the goodness of fit and this means that the correlation
view is
always
for the linear model even when some other model is chosen.
There are two methods of dealing with this. The first is to use another measure of goodness of fit. The second
is to ‘linearize’ the data (discussed on the next page). The calculator provides an alternative measure of
goodness of fit via the
RelErr
value in the
view.
x
i
y
i
1
2
2
4
n
3
8
∑
(
y
−
y
ˆ)
2
i
4
i
=
1
16
RelErr
=
5
32
n
2
∑
y
6
64
i
=
1
i
RelErr
is defined as the measure of the relative error in predicted values when compared to data values, and
has the formula shown right. The smaller the value of
RelErr
the better the fit. The
y
ˆ
values are obtained
using the
PREDY
function internally. The only drawback to
RelErr
is that there is no upper limit its value of
as there is for the correlation coefficient. The interpretation placed on it is that the closer it is to zero the better
the model fits the data. This value is available for any of the data models, including the user defined model.
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