HP 10413 Datasheet Page 146
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146
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
0 8199 1 1662
YX=⋅ +⋅ earlier would use
( 1.1662)
ˆ
0.8199
Y
X
−
=
to predict the X values.
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
yabx=+ is given by the formula:
()
2
xy
x
S
b
S
= .
While the value of
xy
S will not change if the
roles of independent and dependent columns are reversed, the value of
()
2
x
S on the bottom means that this formula will give a different value if you
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.
- Mastering the hp 39g+ 1
- Table of Contents 2
- 76yx x x=−−+ 16
- √35. The 25
- HOME too 27
- Standard mode, very 31
- −− then 33
- 3, 1TT==and 46
- →) into 47
- √(5+Ans) 50
- ENTER will 52
- (-) which is in the same row 55
- The cursor 61
- …and at the 61
- Move to about 63
- it is a 66
- 111xx+−+− 71
- XX= then 3( ) 1( 2( )) 72
- XFFX= will show 72
- 13 13x−≤≤ and 75
- = using 75
- (,, , )a b function X 80
- 1( ) 1FX X 81
- − and then 81
- () 0.5 1gx x=−from x = -2 to 84
- ≥ -2 AND X ≤ 1) 85
- 285 10⋅× then 1/X is 89
- 2 5087719298 10 89
- × . When you 89
- All the normal function 93
- 1( ) 1FX X=− & 94
- 65 65X−≤≤ 97
- . If you wish to 100
- ≤ to 05t 101
- ≤ gives a graph that 101
- () 2 5 2 3vt t t t 104
- 1( ) 4 cos(3 )R 106
- = 2( ) 0.5R 106
- 3( ) 3 2sin(10 )R 106
- T = . If you type it in 107
- 2 1475 10⋅× 109
- 14 29⋅ . This means, of 111
- 16 67⋅ 114
- 252fx x x x=− −+ 115
- 2, , ^ 3 , 4AX X X−= 117
- BC B+=⋅ 118
- *5*AB C B+=⋅ becomes 119
- 2vu ad=− 120
- Σ(I=1,20,RANDOM<0 130
- 0.8199 1.1662yx=+ 139
- 0.693147 142
- YX=⋅ +⋅ earlier would use 146
- Competitor Time 147
- N and of k 148
- N and k 148
- Sample t value is 152
- ↑ and ↓ keys. The size of 165
- → and ← keys 165
- 1.2Px≤ ” 193
- PX x≤ , E9 giving 194
- • HP39/40G (Wire) 198
- • Disk drive… 198
- • Choose the parent aplet; 212
- SETVIEWS 214
- the PLOT 222
- the PLOT view has 222
- VIEWS to see the menu.” 224
- HP39DIR.CUR 226
- HP39DIR.000 226
- (2)(31)xx 244
- −− has been expanded on the 244
- 45 23 17 248
- 4 8723 10⋅× 249
- 0 8199 1 1662YX=⋅ +⋅ 254
- 450xx−−= 257
- 0.0000003 260
- + could be entered into the 262
- {list}) 265
- ∆LIST(L1)={3,3,3,3} 266
- 1x − = 63 269
- (3,4,0) or 4 271
- , , ,...xxx 277
- () 7 6fx x x=−+ 277
- −+−=−+ we 279
- C using the formula 280
- RANDSEED 281
- ()01Px x>=⋅ 282
- () 2 2 1gx x x 284
- POLYROOT 285
- () 4 6fx x x x=− ++… 286
- 5 4 32 23 4 5 290
- N and k and store 292
- 32 0z −=, setting the other 295
- 5sin 5cosri j 297
- 'lim 303
- +++ and 304
- ,: 0.51 1xy y x y x 307
- ≤X AND X≤1) 308
- MAXREAL of 309
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