The goal of this research is to better understand the physical features of starburst galaxies. Radio and X-ray observations are good for exploring the stuff within the central regions of galaxies.  A galaxy that is undergoing a strong star formation, usually in its central area, is known as a starburst galaxy. This paper provides the results of a statistical analysis of a sample of starburst galaxies. The data used in this research have been collected from NASA Extragalactic Database (NED), and HYPERLEDA. Those data have been used to examine possible luminosity correlations of X-ray to a radio of a sample of starburst galaxies. In this research, statistical software, known as statistic-win-program, has been used to investigate if there is a luminosity correlation between multiple-wavelength bands. The results of the statistical analysis conclude that there is a good correlation between X-ray luminosity and radio luminosity at 1.4GHz where the partial correlation coefficient is (R≈0.53) and slope (0.6±0.12). There is also a good correlation between X-ray luminosity and radio luminosity at 5GHz with a good partial correlation coefficient (R ≈ 0.65) and slope (0.77±0.11).  There are good positive relationships between radio luminosity at (1.4GHz, 5GHz) with infrared and far-infrared luminosities (Log L1.4GHz α log LFIR0.89±0.04 α Log LIR0.9±0.03) with a very strong correlation equal to R=0.9 (Log L5GHz α Log LFIR0.79±0.05 α Log LIR0.81±0.05) with strong correlation R=0.8 both with very high probability level p≈10-7. One of the closest and most ubiquitous correlations known among the global features of local star formation and starburst galaxies is the link between far-infrared (FIR) and radio emission.