(15C) Multiple Linear Regression for HP-15C

[Namir]

To perform the regression of the following linear model:

Y = a + bX + cZ

We transform it into the following equations:

(Y-Ymean)/(X-Xmean) = b + c*(Z-Zmean)/(X-Xmean)

Then Calculate a using:

a = Ymean - b*Xmean - c*Zmean

I have added a ZIP file containing the source code for the HP-15C that Torsten recently introduced to this web site (click here).

The drawback for this method is having to enter the data twice. The advantage for this method (over using matrices in the HP-15C to perform multiple regression) is that there is no limit for the number of data points entered.

Memory Map


RCL 0 = Ymean
RCL 1 = Xmean
RCL 8 = Zmean
RCL 9 = X - Xmean

Flags

F0 = When internally set, the program goes into data deletion mode.

Listing

Code:

1 LBL B        # Enter Y before pressing B. Use this label to delete data
2 SF 0        # set flag 0 to delete data
3 LBL A        # Enter Y before pressing A
4 RCL 0
5 -        # Calculate Y - Ymean
6 R/S        # Enter X
7 RCL 1
8 -        # Calculate X - Xmean
9 STO 9
10 /        # Calculate (Y-Ymean)/(X-Xmean)
11 R/S        # Enter Z
12 RCL 8
13 -        # Calculate Z - Zmean
14 RCL 9        
15 /        # Calculate (Z-Zmean)/(X-Xmean)
16 FS? 0        
17 GTO 0
18 Sigma+
19 RTN
20 LBL 0
21 CF 0
22 Sigma-
23 RTN
24 LBL C        # Calculate slope and intercept
25 L.R.
26 R/S
27 RCL 1
28 *        # calculate b*Xmean
29 X<>Y
30 RCL 8
31 *        # calculate c*zmean
32 +        # calculate b*Xmean + c*Zmean
33 CHS
34 RCL 0        
35 +        # calculate a = Ymean - b*Xmean - c*Zmean
36 RTN

Usage

Phase 1

In this phase perform the following:
1. Clear teh statistical registers
2. Enter the values of Y.
3. Calculate the mean value of Y and record it.
4. Clear teh statistical registers
5. Enter the values of X.
6. Calculate the mean value of X and record it.
7. Clear teh statistical registers
8. Enter the values of Z.
9. Calculate the mean value of Z and record it.
10. Clear the statistical registers.
11. Enter teh means for Y, X, and Z in registers 0, 1, and 8 respectively.

Phase 2

1. Enter the value of Y and press the keys f and A.
2. Enter the value of X and press R/S.
3. Enter the value of Z and press R/S.
4. Repeat steps 1 through 3 for all the observations.
5. To calculate the values of coefficients b and c, press the keys f and C. The program, displays the value of coefficient b in the X register.
6. Press the key X<>Y to view and record the value of coefficient c.
7. Press the key X<>Y.
8. Press the key R/S to display the coefficient a.

To delete a data point:
1. Enter the value of Y and press the keys f and B.
2. Enter the value of X and press R/S.
3. Enter the value of Z and press R/S.

Example

Give the following data:

Code:

Y    X    Z
-4.5    1    55
-6.1    2    67
7.1    3.5    33
7.8    4    34
7.7    5    41

In phase 1 calculate the mean for Y as 2.4, the mean for X as 3.1, and the mean for Z as 46. Store these means in registers 0, 1, and 8, respectively.

1. Enter the value of -4.5 and press the keys f and A.
2. Enter the value of 1 and press R/S.
3. Enter the value of 33 and press R/S.
4. Repeat steps 1 through 3 for all the above observations.
5. To calculate the values of coefficients b and c, press the keys f and C. The program, displays the 2.000 as the value of coefficient b in the X register.
6. Press the key X<>Y to view and record -0.30000 as the value of coefficient c.
7. Press the key X<>Y.
8. Press the key R/S to display 10.000 as the coefficient a.

The model is Y = 10 + 2*X - 0.3*Z