In this paper, we explore the physics of the accretion and jet in narrow-line Seyfert 1 galaxies (NLS1). Specifically, we compile a sample composed of 16 nearby NLS1 with $L_{rm bol}/L_{rm Edd} gtrsim 0.1$. We investigate the mutual correlation between their radio luminosity $L_{rm R}$, X-ray luminosity $L_{rm X}$, optical luminosity $L_{rm 5100}$ and black hole mass $M_{rm BH}$. By adopting partial correlation analysis: (1) we find a positive correlation between $L_{rm X}$ and $M_{rm BH}$, and (2) we find a weak positive correlation between $L_{rm R}$ and $L_{5100}$. However, we dont find significant correlations between $L_{rm R}$ and $L_{rm X}$ or between $L_{rm X}$ and $L_{5100}$ after considering the effect of the black hole mass, which leads to a finding of the independence of $L_{rm X}/L_{rm Edd}$ on $L_{5100}/L_{rm Edd}$. Interestingly, the findings that $L_{rm X}$ is correlated with $M_{rm BH}$ and $L_{rm X}/L_{rm Edd}$ is not correlated with $L_{5100}/L_{rm Edd}$ support that the X-ray emission is saturated with increasing $dot{M}$ for $L_{rm bol}/L_{rm Edd} gtrsim 0.1$ in NLS1s, which may be understood in the framework of slim disc scenario. Finally, we suggest that a larger NLS1 sample with high quality radio and X-ray data is needed to further confirm this result in the future.
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