We can estimate the size of the speakers based on their speech sounds alone. We had proposed an auditory computational theory of the Stabilised Wavelet-Mellin Transform (SWMT), which segregates information about the size and shape of the vocal tract and glottal vibration, to explain this observation. It has been shown that the auditory representation or excitation pattern (EP) associated with a weighting function based on the SWMT, termed the ``SSI weight,'' can account for the psychometric functions of size perception. In this study, we investigated whether EP with SSI weight can accurately estimate vocal tract lengths (VTLs) which were measured by magnetic resonance imaging (MRI) in male and female subjects. It was found that the use of SSI weight significantly improved the VTL estimation. Furthermore, the estimation errors in the EP with the SSI weight were significantly smaller than those in the commonly used spectra derived from the Fourier transform, Mel filterbank, and WORLD vocoder. It was also shown that the SSI weight can be easily introduced into these spectra to improve the performance.