Correct Interpretation Of The Predx Function - HP 39g Master Manual

Correct interpretation of the PREDX function

The PREDX function in the MATH menu simply reverses the line of best fit.
For example, the equation ˆ
−
( Y 1.1662)
=
ˆ
to predict the X values.
X
0.8199
Whether this is mathematically correct depends on how you interpret the
PREDX function. If, as HP intended, you interpret it to mean "give me an x
value which, if used in the PREDY function, would give me this y value", then
it is correct. However, it should not be interpreted to mean "predict an x
value based on this y value".
It should not be felt that the hp 39g+ is unusual in this interpretation. Most
calculators' equivalent of the PREDX function behave in the same manner.
The reason for not using the second interpretation is that the results it gives
would then be incorrect. The line of best fit (unlike the correlation) changes
as the independent and dependent variables swap roles and can't be simply
reversed in this way.
The formula for the slope b in the line of best
= +
fit ˆ y a bx is given by the formula:
While the value of
roles of independent and dependent columns are reversed, the value of
( )
2
on the bottom means that this formula will give a different value if you
S
x
change which column is regarded as x (indep.) and which as y (dependent).
This different value for b will also mean a different value for a and these will
not be the values which would result from the simple inverse function.
If you truly wish to predict X values in the sense of the second interpretation,
then you should change to the SYMB view and enter a new data set S2 which
uses C2 and C1 in reversed order, avoiding the need to re-enter the data.
Now use PREDY rather than PREDX. As you
can see in the screen below, the result of
PREDX(5) with C1 vs. C2 is not the same as
PREDY(5) using C2 vs. C1.
= ⋅
Y 0 8199 X
b
S will not change if the
xy
146
+ ⋅
earlier would use
1 1662
S
=
.
xy
( )
2
S
x