Scatterplot and Correlation of table variables

Hello there

Q = readtable("DA.xlsx")

Q = 20×18 table
    Tam      Az     Clp      Dp     DH     DN     EB     GH      Pw     Sd     Prs     WD     WV      AD     ZT      La        Lo      Al 
    ____    ____    ____    ____    ___    ___    ___    ___    ____    __    _____    ___    ___    ____    ___    _____    ______    ___

    22.7    -143      41    21.8      0      0      0      0    3.44    0     916.2    294      1    0.11    155    4.156    9.2632    707
    22.5    -126    21.4    21.7      0      0      0      0    3.37    0     915.7    291      1    0.11    144    4.156    9.2632    707
      22    -118       0    21.3      0      0      0      0     3.3    0     915.5    299    0.9    0.11    132    4.156    9.2632    707
    21.8    -114       0    21.1      0      0      0      0    3.26    0     915.7    301    0.9    0.11    118    4.156    9.2632    707
    21.6    -113       0    20.9      0      0      0      0    3.22    0     915.9    295    0.7    0.11    104    4.156    9.2632    707
    21.7    -113       0      21      7      0      0      7    3.16    0     916.1    290    0.6    0.11     91    4.156    9.2632    707
    22.2    -115       0      21     81     27     27     84    3.12    0     916.7    295    0.5    0.11     77    4.156    9.2632    707
    23.6    -118    13.4    21.5    183    168    134    190    3.14    0     917.4     36    0.3    0.11     64    4.156    9.2632    707
      25    -125    22.2    21.8    311    272    214    311     3.2    0     917.5    102    0.9    0.11     51    4.156    9.2632    707
      26    -136    20.1    21.4    457    371    347    457    3.27    0       917    120    1.1    0.11     39    4.156    9.2632    707
      27    -154    21.8    21.1    536    465    365    536    3.32    0     916.4    133    1.1    0.11     31    4.156    9.2632    707
    27.6     178    22.6      21    566    508    488    566    3.36    0     915.8    154    1.2    0.11     28    4.156    9.2632    707
    27.6     151    30.5    21.2    506    442    441    506    3.38    0       915    175    1.2    0.11     32    4.156    9.2632    707
    27.5     134    42.7    21.3    361    360    354    361    3.39    0     914.4    199    1.1    0.11     41    4.156    9.2632    707
    27.2     124    32.4    21.2    313    246    211    313    3.43    0       914    218    1.3    0.11     53    4.156    9.2632    707
    26.6     118    17.8      21    209    119     98    221    3.46    0     913.8    233    1.6    0.11     65    4.156    9.2632    707

x=[Q.Tam,Q.Az,Q.Clp,Q.Dp,Q.DH,Q.DN,Q.EB, Q.Pw ,Q.Sd,Q.Prs,Q.WD,Q.WV,Q.AD, Q.ZT, Q.La, Q.Lo, Q.Al];
y=[Q.GH];
mdl=fitlm(x,y)

Warning: Regression design matrix is rank deficient to within machine precision.

mdl = 
Linear regression model:
    y ~ 1 + x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 + x12 + x13 + x14 + x15 + x16 + x17

Estimated Coefficients:
                    Estimate        SE         tStat       pValue  
                   __________    ________    _________    _________

    (Intercept)             0           0          NaN          NaN
    x1                 2.0783      5.6941      0.36499       0.7501
    x2              0.0055895    0.018668      0.29942      0.79287
    x3              -0.079915     0.20744     -0.38525      0.73717
    x4                -4.7595      6.9256     -0.68723      0.56293
    x5                  1.044    0.053721       19.434    0.0026374
    x6              -0.068095    0.062486      -1.0898      0.38962
    x7             -0.0045757      0.0573    -0.079855      0.94362
    x8                 22.631      45.981      0.49218      0.67131
    x9                      0           0          NaN          NaN
    x10               0.84604      3.6954      0.22894      0.84019
    x11             -0.033195    0.032357      -1.0259      0.41281
    x12               -9.5612      9.7954     -0.97609      0.43196
    x13                     0           0          NaN          NaN
    x14              0.043679     0.14711      0.29692      0.79452
    x15                     0           0          NaN          NaN
    x16                     0           0          NaN          NaN
    x17               -1.1029      4.9284     -0.22378      0.84371


Number of observations: 20, Error degrees of freedom: 7
Root Mean Squared Error: 3.03
R-squared: 1,  Adjusted R-Squared: 1
F-statistic vs. constant model: 7.6e+03, p-value = 3.38e-13

corrplot(Q)

Error using corrplot
One or more variables show no variation. Correlations undefined.

Please why does the pvalue for X9, X13, X15, X16 return NaN and not X17 even though X17 have the same values all through.?

Also how do I get how do I get scatter plot and how can I fix the correlation of Input variables with output GH?

Answer 1

[Pratyush]

Hi Mbunya.

It is my understanding that you are trying to fit a linear model to the data stored in x with y as the ground truth. However, you are getting NaN as the value of some weights after fittting a linear model. I have analysed your data and I feel the problem seems to be occuring because of the following reason.

Some columns in your data - Sd, AD, La, Lo and Al have the same value at all data samples. There are two problems that will occur because of this while fitting a linear model.

1. The matrix used to fit a linear model by will become rank deficient. When we try to fit a linear model with the above mentioned fields, MATLAB will throw a warning that the Regression design matrix is rank deficient.
2. Also, the above mentioned fields do not add any value to the model fitting. If some property is same at all data samples, its value has no importance in deciding the output of the model for any sample. It is a constant property.

I retrained the model using your data after removing the above mentioned constant properties as shown below.

x=[Q.Tam,Q.Az,Q.Clp,Q.Dp,Q.DH,Q.DN,Q.EB, Q.Pw ,Q.Prs,Q.WD,Q.WV, Q.ZT];
y=[Q.GH];
mdl=fitlm(x,y)

This time no NaN vaues were observed for any weights or the intercepts in the linear model as shown in the image below. Hope this resolves your problem.

Here are some additional resources to help you with linear regression.

Linear Regression in Matrix Format

Fit linear regression model - MATLAB fitlm (mathworks.com)

[MBUNYA NERVILLE ANYANG]

Ok, thank you very much