MATLAB: Statistics toolbox predict new data non linear regression

non-linear regressiontoolbox

Hi!
After building a non linear model, the example in the matlab statistics toolbox predicts new data. I dont understand
'Xnew =  [200,200,200;100,200,100;500,50,5];'
– we have 3 columns with each 13 rows and our output rate. Why does this row has 9 values? And what does ypred?
Please see below the example:
This is our data (X):
470  300  10
285  80  10
470  300  120
470  80  120
470  80  10
100  190  10
100  80  65
470  190  65
100  300  54
100  300  120
100  80  120
285  300  10
285  190  120
Data output(Y):
8.55000000000000
3.79000000000000
4.82000000000000
0.0200000000000000
2.75000000000000
14.3900000000000
2.54000000000000
4.35000000000000
13
8.50000000000000
0.0500000000000000
11.3200000000000
3.13000000000000
…. (Building model – Step 1-5)….
Step 6. Predict for new data
Create some new data and predict the response from both models.
Xnew =  [200,200,200;100,200,100;500,50,5];
[ypred yci] = predict(mdl,Xnew)
ypred =
      1.8762
      6.2793
      1.6718
yci =
      1.6283    2.1242
      5.9789    6.5797
      1.5589    1.7846
  [ypred1 yci1] = predict(mdl1,Xnew)
  ypred1 =
      1.8984
      6.2555
      1.6594
yci1 =
      1.6260    2.1708
      5.9323    6.5787
      1.5345    1.7843
Even though the model coefficients are dissimilar, the predictions are nearly identical.
Thank you!

Best Answer

They estimate a non-linear model that has three independent variables (input variables) and five coefficients. Then they predict, that means they calculate the output for certain values of the input variables. For an output value they have to feed the values with three input values because the model contains three independent variables. They do that three times. They caluclate three output values, that is why the matrix for the input variables is a 3 x 3 matrix: three times the three values for the input variables. So Xnew is not a row vector of 9 elements as you write in your question but a 3 x 3 matrix. The variable ypred contains the three values of the output variable that were calcualted based on the matrix Xnew.
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