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I have built a PLS model on a training set and I have tried to predict a validation set. From the correlation between real values and predicted, the PLS model seems to have some predictive capabilities (not great but good enough for me). The Pearson's correlation coefficient is of $0.575$.

Unfortunately, when I tried to calculate the $Q^2 = 1-\dfrac{ \sum(y_i - \hat y_i)^2 }{ \sum(y_i - \bar y)^2 } $, its value is negative: $Q^2=-0.00778$.

I suppose that I got negative value because some samples are predicted higher or lower than the range of real values.

Is $Q^2$ really a good indicator for my prediction?

PLS regression

Dave
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Stefano Cacciatore
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  • Of possible interest. $Q^2<0$ means that the model is not very good and performs worse than you would do by always predicting $\bar y$. // You might be interested in plotting your real and predicted values on top of the scatterplot in a different color. – Dave May 03 '22 at 17:14

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