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
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