Generating nonlinear multiple regression equations

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Generating nonlinear multiple regression equations

samith95
I have 4 variables such as x, y, z, and w. I used trees.M5P model to run multiple non-linear rgreation. I got the result. but I can not understand that result. I want to derive equastion. i have attached my result. please tell me what are the 26 rules that they have used and how I can derive the values for my equation. help me, sir.

Result
=== Run information ===

Scheme:       weka.classifiers.trees.M5P -M 4.0
Relation:     test03
Instances:    750
Attributes:   4
              LU_Index
              Density
              Accessibilty
              TA
Test mode:    10-fold cross-validation

=== Classifier model (full training set) ===

M5 pruned model tree:
(using smoothed linear models)

TA <= 380.204 :
|   Accessibilty <= 8600.059 :
|   |   Density <= 214.465 :
|   |   |   Density <= 186.069 : LM1 (52/90.603%)
|   |   |   Density >  186.069 : LM2 (24/106.404%)
|   |   Density >  214.465 :
|   |   |   Density <= 388.602 :
|   |   |   |   TA <= 152.109 :
|   |   |   |   |   Accessibilty <= 4630.453 :
|   |   |   |   |   |   Accessibilty <= 3876.62 : LM3 (4/29.816%)
|   |   |   |   |   |   Accessibilty >  3876.62 : LM4 (4/75.902%)
|   |   |   |   |   Accessibilty >  4630.453 : LM5 (7/15.683%)
|   |   |   |   TA >  152.109 :
|   |   |   |   |   Density <= 268.399 : LM6 (22/56.48%)
|   |   |   |   |   Density >  268.399 : LM7 (14/42.732%)
|   |   |   Density >  388.602 : LM8 (13/78.733%)
|   Accessibilty >  8600.059 :
|   |   Accessibilty <= 16846.539 :
|   |   |   Density <= 273.599 :
|   |   |   |   Accessibilty <= 13290.31 : LM9 (22/69.596%)
|   |   |   |   Accessibilty >  13290.31 : LM10 (11/100.604%)
|   |   |   Density >  273.599 : LM11 (11/69.675%)
|   |   Accessibilty >  16846.539 : LM12 (16/76.926%)
TA >  380.204 :
|   Accessibilty <= 11711.168 :
|   |   Density <= 219.572 : LM13 (129/105.234%)
|   |   Density >  219.572 :
|   |   |   Density <= 470.158 : LM14 (161/80.996%)
|   |   |   Density >  470.158 :
|   |   |   |   Density <= 943.497 : LM15 (36/116.592%)
|   |   |   |   Density >  943.497 : LM16 (12/71.795%)
|   Accessibilty >  11711.168 :
|   |   TA <= 1538.094 :
|   |   |   TA <= 1049.712 :
|   |   |   |   Accessibilty <= 14945.302 : LM17 (42/56.616%)
|   |   |   |   Accessibilty >  14945.302 :
|   |   |   |   |   Accessibilty <= 17037.705 : LM18 (16/32.316%)
|   |   |   |   |   Accessibilty >  17037.705 :
|   |   |   |   |   |   Density <= 374.708 :
|   |   |   |   |   |   |   Density <= 290.032 : LM19 (27/63.168%)
|   |   |   |   |   |   |   Density >  290.032 : LM20 (8/63.959%)
|   |   |   |   |   |   Density >  374.708 : LM21 (10/41.743%)
|   |   |   TA >  1049.712 : LM22 (33/65.912%)
|   |   TA >  1538.094 :
|   |   |   Accessibilty <= 16472.554 :
|   |   |   |   Accessibilty <= 13369.648 : LM23 (12/69.638%)
|   |   |   |   Accessibilty >  13369.648 : LM24 (23/103.6%)
|   |   |   Accessibilty >  16472.554 :
|   |   |   |   Density <= 380.803 : LM25 (31/60.534%)
|   |   |   |   Density >  380.803 : LM26 (10/55.233%)

LM num: 1
LU_Index =
        0.0002 * Accessibilty
        + 0 * TA
        + 0.2584

LM num: 2
LU_Index =
        0.0003 * Accessibilty
        + 0 * TA
        + 0.2807

LM num: 3
LU_Index =
        0.0001 * Accessibilty
        - 0.0001 * TA
        + 0.2821

LM num: 4
LU_Index =
        0.0001 * Accessibilty
        - 0 * TA
        + 0.2723

LM num: 5
LU_Index =
        0.0001 * Accessibilty
        + 0 * TA
        + 0.2523

LM num: 6
LU_Index =
        0.0001 * Accessibilty
        + 0 * TA
        + 0.2842

LM num: 7
LU_Index =
        0.0001 * Accessibilty
        - 0.0001 * TA
        + 0.3191

LM num: 8
LU_Index =
        -0 * Accessibilty
        + 0 * TA
        + 0.2772

LM num: 9
LU_Index =
        0 * Accessibilty
        - 0 * TA
        + 0.3755

LM num: 10
LU_Index =
        0 * Accessibilty
        - 0 * TA
        + 0.3728

LM num: 11
LU_Index =
        -0.0001 * Density
        + 0.0001 * Accessibilty
        - 0 * TA
        + 0.4255

LM num: 12
LU_Index =
        -0 * Accessibilty
        + 0 * TA
        + 0.3539

LM num: 13
LU_Index =
        -0 * Accessibilty
        + 0 * TA
        + 0.3664

LM num: 14
LU_Index =
        -0 * Accessibilty
        + 0 * TA
        + 0.423

LM num: 15
LU_Index =
        -0 * Accessibilty
        + 0 * TA
        + 0.411

LM num: 16
LU_Index =
        -0 * Accessibilty
        + 0 * TA
        + 0.3629

LM num: 17
LU_Index =
        -0 * Accessibilty
        + 0 * TA
        + 0.4131

LM num: 18
LU_Index =
        -0 * Accessibilty
        + 0 * TA
        + 0.4532

LM num: 19
LU_Index =
        0 * Accessibilty
        + 0 * TA
        + 0.431

LM num: 20
LU_Index =
        0 * Accessibilty
        + 0 * TA
        + 0.4321

LM num: 21
LU_Index =
        -0 * Density
        - 0.0001 * Accessibilty
        + 0 * TA
        + 0.4193

LM num: 22
LU_Index =
        -0 * Accessibilty
        + 0 * TA
        + 0.4503

LM num: 23
LU_Index =
        -0 * Accessibilty
        - 0 * TA
        + 0.5424

LM num: 24
LU_Index =
        -0 * Accessibilty
        - 0 * TA
        + 0.4765

LM num: 25
LU_Index =
        -0.0001 * Accessibilty
        + 0 * TA
        + 0.438

LM num: 26
LU_Index =
        -0 * Density
        - 0.0001 * Accessibilty
        + 0 * TA
        + 0.4396

Number of Rules : 26

Time taken to build model: 0.07 seconds

=== Cross-validation ===
=== Summary ===

Correlation coefficient                 -0.0448
Mean absolute error                      0.3331
Root mean squared error                  0.5682
Relative absolute error                348.8296 %
Root relative squared error            473.0286 %
Total Number of Instances              750   

--

Best Regards

 

Samith Madusanka | Undergraduate

University of Moratuwa

Mobile     : 0714953771

E-mail     : [hidden email] 

               : 152324J[hidden email]

Fb Pg      : https://www.facebook.com/Fun-Tech-134029907288749/

 

** Less Pollution is the Best Solution**





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Re: Generating nonlinear multiple regression equations

Eibe Frank-2
Administrator
You should read up on decision tree models so that you can understand how to interpret them. An M5P tree is a decision tree with linear regression models at the leaf nodes. It gives you piecewise linear model of the unknown function.

Cheers,
Eibe

> On 29/09/2019, at 10:03 PM, Samith Madusanka <[hidden email]> wrote:
>
> I have 4 variables such as x, y, z, and w. I used trees.M5P model to run multiple non-linear rgreation. I got the result. but I can not understand that result. I want to derive equastion. i have attached my result. please tell me what are the 26 rules that they have used and how I can derive the values for my equation. help me, sir.
>
> Result
> === Run information ===
>
> Scheme:       weka.classifiers.trees.M5P -M 4.0
> Relation:     test03
> Instances:    750
> Attributes:   4
>               LU_Index
>               Density
>               Accessibilty
>               TA
> Test mode:    10-fold cross-validation
>
> === Classifier model (full training set) ===
>
> M5 pruned model tree:
> (using smoothed linear models)
>
> TA <= 380.204 :
> |   Accessibilty <= 8600.059 :
> |   |   Density <= 214.465 :
> |   |   |   Density <= 186.069 : LM1 (52/90.603%)
> |   |   |   Density >  186.069 : LM2 (24/106.404%)
> |   |   Density >  214.465 :
> |   |   |   Density <= 388.602 :
> |   |   |   |   TA <= 152.109 :
> |   |   |   |   |   Accessibilty <= 4630.453 :
> |   |   |   |   |   |   Accessibilty <= 3876.62 : LM3 (4/29.816%)
> |   |   |   |   |   |   Accessibilty >  3876.62 : LM4 (4/75.902%)
> |   |   |   |   |   Accessibilty >  4630.453 : LM5 (7/15.683%)
> |   |   |   |   TA >  152.109 :
> |   |   |   |   |   Density <= 268.399 : LM6 (22/56.48%)
> |   |   |   |   |   Density >  268.399 : LM7 (14/42.732%)
> |   |   |   Density >  388.602 : LM8 (13/78.733%)
> |   Accessibilty >  8600.059 :
> |   |   Accessibilty <= 16846.539 :
> |   |   |   Density <= 273.599 :
> |   |   |   |   Accessibilty <= 13290.31 : LM9 (22/69.596%)
> |   |   |   |   Accessibilty >  13290.31 : LM10 (11/100.604%)
> |   |   |   Density >  273.599 : LM11 (11/69.675%)
> |   |   Accessibilty >  16846.539 : LM12 (16/76.926%)
> TA >  380.204 :
> |   Accessibilty <= 11711.168 :
> |   |   Density <= 219.572 : LM13 (129/105.234%)
> |   |   Density >  219.572 :
> |   |   |   Density <= 470.158 : LM14 (161/80.996%)
> |   |   |   Density >  470.158 :
> |   |   |   |   Density <= 943.497 : LM15 (36/116.592%)
> |   |   |   |   Density >  943.497 : LM16 (12/71.795%)
> |   Accessibilty >  11711.168 :
> |   |   TA <= 1538.094 :
> |   |   |   TA <= 1049.712 :
> |   |   |   |   Accessibilty <= 14945.302 : LM17 (42/56.616%)
> |   |   |   |   Accessibilty >  14945.302 :
> |   |   |   |   |   Accessibilty <= 17037.705 : LM18 (16/32.316%)
> |   |   |   |   |   Accessibilty >  17037.705 :
> |   |   |   |   |   |   Density <= 374.708 :
> |   |   |   |   |   |   |   Density <= 290.032 : LM19 (27/63.168%)
> |   |   |   |   |   |   |   Density >  290.032 : LM20 (8/63.959%)
> |   |   |   |   |   |   Density >  374.708 : LM21 (10/41.743%)
> |   |   |   TA >  1049.712 : LM22 (33/65.912%)
> |   |   TA >  1538.094 :
> |   |   |   Accessibilty <= 16472.554 :
> |   |   |   |   Accessibilty <= 13369.648 : LM23 (12/69.638%)
> |   |   |   |   Accessibilty >  13369.648 : LM24 (23/103.6%)
> |   |   |   Accessibilty >  16472.554 :
> |   |   |   |   Density <= 380.803 : LM25 (31/60.534%)
> |   |   |   |   Density >  380.803 : LM26 (10/55.233%)
>
> LM num: 1
> LU_Index =
>         0.0002 * Accessibilty
>         + 0 * TA
>         + 0.2584
>
> LM num: 2
> LU_Index =
>         0.0003 * Accessibilty
>         + 0 * TA
>         + 0.2807
>
> LM num: 3
> LU_Index =
>         0.0001 * Accessibilty
>         - 0.0001 * TA
>         + 0.2821
>
> LM num: 4
> LU_Index =
>         0.0001 * Accessibilty
>         - 0 * TA
>         + 0.2723
>
> LM num: 5
> LU_Index =
>         0.0001 * Accessibilty
>         + 0 * TA
>         + 0.2523
>
> LM num: 6
> LU_Index =
>         0.0001 * Accessibilty
>         + 0 * TA
>         + 0.2842
>
> LM num: 7
> LU_Index =
>         0.0001 * Accessibilty
>         - 0.0001 * TA
>         + 0.3191
>
> LM num: 8
> LU_Index =
>         -0 * Accessibilty
>         + 0 * TA
>         + 0.2772
>
> LM num: 9
> LU_Index =
>         0 * Accessibilty
>         - 0 * TA
>         + 0.3755
>
> LM num: 10
> LU_Index =
>         0 * Accessibilty
>         - 0 * TA
>         + 0.3728
>
> LM num: 11
> LU_Index =
>         -0.0001 * Density
>         + 0.0001 * Accessibilty
>         - 0 * TA
>         + 0.4255
>
> LM num: 12
> LU_Index =
>         -0 * Accessibilty
>         + 0 * TA
>         + 0.3539
>
> LM num: 13
> LU_Index =
>         -0 * Accessibilty
>         + 0 * TA
>         + 0.3664
>
> LM num: 14
> LU_Index =
>         -0 * Accessibilty
>         + 0 * TA
>         + 0.423
>
> LM num: 15
> LU_Index =
>         -0 * Accessibilty
>         + 0 * TA
>         + 0.411
>
> LM num: 16
> LU_Index =
>         -0 * Accessibilty
>         + 0 * TA
>         + 0.3629
>
> LM num: 17
> LU_Index =
>         -0 * Accessibilty
>         + 0 * TA
>         + 0.4131
>
> LM num: 18
> LU_Index =
>         -0 * Accessibilty
>         + 0 * TA
>         + 0.4532
>
> LM num: 19
> LU_Index =
>         0 * Accessibilty
>         + 0 * TA
>         + 0.431
>
> LM num: 20
> LU_Index =
>         0 * Accessibilty
>         + 0 * TA
>         + 0.4321
>
> LM num: 21
> LU_Index =
>         -0 * Density
>         - 0.0001 * Accessibilty
>         + 0 * TA
>         + 0.4193
>
> LM num: 22
> LU_Index =
>         -0 * Accessibilty
>         + 0 * TA
>         + 0.4503
>
> LM num: 23
> LU_Index =
>         -0 * Accessibilty
>         - 0 * TA
>         + 0.5424
>
> LM num: 24
> LU_Index =
>         -0 * Accessibilty
>         - 0 * TA
>         + 0.4765
>
> LM num: 25
> LU_Index =
>         -0.0001 * Accessibilty
>         + 0 * TA
>         + 0.438
>
> LM num: 26
> LU_Index =
>         -0 * Density
>         - 0.0001 * Accessibilty
>         + 0 * TA
>         + 0.4396
>
> Number of Rules : 26
>
> Time taken to build model: 0.07 seconds
>
> === Cross-validation ===
> === Summary ===
>
> Correlation coefficient                 -0.0448
> Mean absolute error                      0.3331
> Root mean squared error                  0.5682
> Relative absolute error                348.8296 %
> Root relative squared error            473.0286 %
> Total Number of Instances              750  
>
> --
> Best Regards
>  
> Samith Madusanka | Undergraduate
> University of Moratuwa
> Mobile     : 0714953771
> E-mail     : [hidden email]
>                : [hidden email]
> Fb Pg      : https://www.facebook.com/Fun-Tech-134029907288749/
>  
> ** Less Pollution is the Best Solution**
>
>
>
> _______________________________________________
> Wekalist mailing list -- [hidden email]
> Send posts to: To unsubscribe send an email to [hidden email]
> To subscribe, unsubscribe, etc., visit
> https://list.waikato.ac.nz/postorius/lists/wekalist.list.waikato.ac.nz
> List etiquette: http://www.cs.waikato.ac.nz/~ml/weka/mailinglist_etiquette.html
_______________________________________________
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