(11C) Multiple Linear Regression for HP-11C

[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

Memory Map


RCL 6 = Ymean
RCL 7 = 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 6
5 -        # Calculate Y - Ymean
6 R/S        # Enter X
7 RCL 7
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 7
28 *        # calculate b*Xmean
29 X<>Y
30 RCL 8
31 *        # calculate c*zmean
32 +        # calculate b*Xmean + c*Zmean
33 CHS
34 RCL 6        
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 6, 7, 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 6, 7, 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