Violation of homoscedasticity assumption in a Panel Data Regression Model (PDRM) implies unequal variability of error terms, and this creates heterogeneity problem in estimation. This research thus attempts to investigate the presence and effect of heteroscedasticity in panel data through the estimation of a specified audit fees PDRM using Pooled ordinary least square (POLS, Least square dummy variable (LSDV) technique where all coefficients vary across individual and Random Effect estimator (REM). A conditional Lagrange multiplier test was developed via a two-way error components model, to examine the presence of heteroscedasticity in the fitted POLS model while Hausman test was used to ascertain the suitability of the LSDV Model over Random effect model and vice-versa. The conditional LM test gave a value of 7.1462 with P-value of 0.000000000000446 which shows that there is presence of unequal variance of MA(1) errors among the residuals of the fitted Pooled OLS model, thereby rendered the estimator inconsistent. Both LSDV and RE models were fitted to take care of the challenges posed by the presence of heteroscedasticity and both models captured the goodness of fit better when compared to the Pooled OLS model. However, the Hausman test revealed that random effect model will not be preferable since p-value of the former is less than 0.05.