Yapay sinir aglari ile satis tahmini problemi cozdugumde R2 degerinin negatif cikmasi ne ifade ediyor. R2 degeri hangi aralikta olmalidir?

[Walter Roberson]

Approximate translation:

What does it mean when the R2 value is negative when I solve the sales forecasting problem with artificial neural networks. What range should the R2 value be in?

[Walter Roberson]

A negative indicates that the model is worse than random in predicting the data.

https://www.mathworks.com/help/curvefit/evaluating-goodness-of-fit.html

Note that it is possible to get a negative R-square for equations that do not contain a constant term. Because R-square is defined as the proportion of variance explained by the fit, if the fit is actually worse than just fitting a horizontal line then R-square is negative. In this case, R-square cannot be interpreted as the square of a correlation. Such situations indicate that a constant term should be added to the model.

[Torsten]

Approximate translation :-)

Negatif, modelin verileri tahmin etmede rastgeleden daha kötü olduğunu gösterir.

https://www.mathworks.com/help/curvefit/evaluating-goodness-of-fit.html

Sabit terim içermeyen denklemler için negatif bir R-kare elde etmenin mümkün olduğuna dikkat edin. R-kare, uyum tarafından açıklanan varyans oranı olarak tanımlandığından, eğer uyum aslında yatay bir çizgiyi sığdırmaktan daha kötüyse, R-kare negatiftir. Bu durumda, R-kare bir korelasyonun karesi olarak yorumlanamaz. Bu gibi durumlar modele bir sabit terim eklenmesi gerektiğini göstermektedir.

[John D'Errico]

Walter is correct. A negative R^2 is a typical symptom of a model that lacks a constant term, but in fact, it could really use a constant term. Essentially it tells you that your model predicts more poorly than just using a constant predictor for your model.

[the cyclist]

A minor correction for posterity:

It's not that negative R^2 indicates that the model is worse than random in predicting the data. It's worse than using the mean response as the prediction for all observations. This is the "horizontal line" mentioned in the documentation that @Walter Roberson quoted.

The reason the mean is relevant is that it is the baseline from which the "total sum of squares" of the data is calculated, which in turn enters into the calculation of R^2.

Answer 1

[John D'Errico]

Let me give an example.

x = rand(100,1);
y = 5 - 3*x + randn(size(x));
plot(x,y,'o')

First, fit a LINEAR polynomial model to the data.

[mdl,gof] = fit(x,y,'poly1')

mdl = 
     Linear model Poly1:
     mdl(x) = p1*x + p2
     Coefficients (with 95% confidence bounds):
       p1 =      -2.891  (-3.556, -2.227)
       p2 =       4.757  (4.359, 5.155)

gof = struct with fields:
           sse: 88.4065
       rsquare: 0.4319
           dfe: 98
    adjrsquare: 0.4261
          rmse: 0.9498

So this model has an r^2 value of 0.4319. Compare that to a model that completely lacks a constant term.

ft = fittype('a*x','indep','x');
[mdlnocon,gofnocon] = fit(x,y,ft)

Warning: Start point not provided, choosing random start point.

mdlnocon = 
     General model:
     mdlnocon(x) = a*x
     Coefficients (with 95% confidence bounds):
       a =       4.108  (3.295, 4.922)

gofnocon = struct with fields:
           sse: 596.3427
       rsquare: -2.8321
           dfe: 99
    adjrsquare: -2.8321
          rmse: 2.4543

Here the R^2 is a strange looking -2.8. And yes, R^2 is always supposed to be between 0 and 1. But what you need to understand is that ONLY applies when you have a constant term in your model. Otherwise, R^2 is complete gibberish for a model with no constant term.