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The unbiased estimation of the fraction of variance explained by a model

Fig 7

Applying our unbiased estimator with CIs to fit four example MT neuronal direction tuning curves to a sinusoidal model.

(A) Example neuron tuning curve (orange trace with SEM bars) with excellent fit to sinusoidal model (blue trace, ), high SNR and tight CI (parameters specified above plot panel). (B) Example neuron with poor fit to sinusoidal model but with a reasonable SNR and narrow CI that provide confidence that the neuronal tuning systematically deviates from the model. (C) Example neuron with poor SNR and wild estimate of , which is reflected in large CI = [0.3, 1], suggesting that no conclusion can be made about how well the model describes any actual tuning here. (D) Example neuron with a seemingly reasonable , but the low SNR and CI covering the entire interval [0, 1] reveals that this fit cannot be trusted.

doi: https://doi.org/10.1371/journal.pcbi.1009212.g007