HP 12C: An Improved Linear Regression Function (from Curvee RPN-45 SD)
Curvee RPN-45 Simulator
The Curvee RPN-45 from Curvee Software is an excellent app. The RPN-45 SD app is the Super-45. The Super-45 is a emulator of the classic HP 45 calculator from 1973 with the following enhancements:
* The gold shift key becomes a double-shift key (gold/purple)
* Complex Numbers
* 10 additional registers
* Days between dates
* Four solvers: 2 x 2 system of linear equations, 3 x 3 system of linear equations, quadratic equation, cubic equation
* Expanded statistics including full linear regression analysis
I have purchased one on my iPod Touch (that is an iPhone without the "phone" part) for $1.99 (prices may vary). There are versions for the iPhone and iPad.
For more information: http://cuveesoft.ch/rpn45/en/index.html
The enhanced linear regression (L.R.) function on the Super-45 returns the following calculations to the four-level stack:
T: covariance
Z: correlation
Y: slope
X: intercept
The relationship between correlation (r) and covariance (cov):
cov(x,y) = r * sx * sy
sx = standard deviation of x-data
sy = standard deviation of y-data
The HP 12C mimics the enhanced L.R. function. Yes, check out this app!
HP 12C Program: Enhanced Linear Regression
The results are stored in the following registers:
R7 = intercept
R8 = Slope
R9 = correlation
R.0 = covariance
In addition, I added code to calculate population deviation: σx in the x-stack, σy in the y-stack.
Step #: Code [ key ]
// linear regression function
01: 1 [ 1 ]
02: 43, 1 [ x^,r ]
03: 34 [ x<>y ]
04: 44, 9 [ STO 9 ]
05: 43, 48 [ s ]
06: 20 [ × ]
07: 20 [ × ]
08: 44, 48, 0 [ STO . 0 (decimal point, zero) ]
09: 0 [ 0 ]
10: 43, 2 [ y^, r ]
11: 44, 7 [ STO 7 ]
12: 1 [ 1 ]
13: 43, 2 [ y^, r ]
14: 34 [ x<>y ]
15: 33 [ R↓ ]
16: 34 [ x<>y ]
17: 30 [ - ]
18: 44, 8 [ STO 8 ]
19: 45, 48, 0 [ RCL . 0 (decimal point, zero) ]
20: 45, 9 [ RCL 9 ]
21: 45, 8 [ RCL 8 ]
22: 45, 7 [ RCL 7 ]
23: 43, 33, 00 [ GTO 00 ]
// population deviation
24: 45, 1 [ RCL 1 ]
25: 36 [ ENTER ]
26: 36 [ ENTER ]
27: 1 [ 1 ]
28: 30 [ - ]
29: 10 [ ÷ ]
30: 43, 21 [ √ ]
31: 44, 0 [ STO 0 ]
32: 43, 48 [ s ]
33: 45, 0 [ RCL 0 ]
34: 10 [ ÷ ]
35: 34 [ x<>y ]
36: 45, 0 [ RCL 0 ]
37: 10 [ ÷ ]
38: 34 [ x<>y ]
39: 43, 33, 00 [ GTO 00 ]
Example
Fix 6 mode is set.
Data:
(5.35, 10)
(5,70, 11)
(6.18, 12)
(6.55, 13)
(6.97, 14)
(7.36, 15)
After entering the data points:
[ f ] (PRGM) [ R/S ]
-3.162788 (intercept), [ R↓ ]
2.465287 (slope), [ R↓ ]
0.999396 (correlation, r), [ R↓ ]
1.418000 (covariance) ( [ R↓ ] to return the stack to it's original configuration )
[ g ] (GTO) 24 [ R/S ]
0.692331 ( σx ) [ x<>y ]
1.707825 ( σy )
Eddie
All original content copyright, © 2011-2023. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
