The objective of this paper is to provide an empirical comparison between a linear dimensionality reduction technique, referred to as principal component analysis (PCA), and a nonlinear dimensionality reduction technique, that is, kernel principal component analysis (KPCA), used as a preprocessing step for nonparametric regression. The reason for this contrast is the curse of dimensionality, which is likely to worsen the performance of nonparametric regression with an increasing number of explanatory variables. However, although KPCA constitutes a nonlinear analog of PCA, this does not imply that KPCA would always necessarily provide better predictive performance than PCA, given that there are nonlinear terms involved in the regression function. Thus, we study the scenarios where PCA is good enough and those where KPCA is expected to bring some improvements in accuracy. Using Monte Carlo simulation, the present study was performed with varying sample sizes (n = 20, 60, 150), numbers of explanatory variables (p = 5, 10), and numbers of retained components (q = 2, 4) in the R environment. Three regression functions with increasingly complex nonlinearity were considered, with predictors and random errors drawn i.i.d. from normal distributions. After the dimensionality reduction, the Nadaraya–Watson kernel regression estimator was estimated using the components derived from PCA and KPCA, where a Gaussian kernel was used in both steps. The predictive performance was evaluated using the Average Prediction Error (APE) and Mean Squared Prediction Error (MSPE) for 500 Monte Carlo replications for each simulation setting. The results show that the predictive performance improves with the number of retained components, from q = 2 to q = 4, and that larger sample sizes tend to decrease both APE and MSPE. For a fixed number of retained components, increasing the number of explanatory variables generally leads to higher prediction errors. The PCA vs. KPCA comparison does not show a consistent superiority of one over the other, but their relative performance depends on the sample size, predictor dimension, number of retained components, and the nonlinearity structure of the regression function....................... Keywords:.................. Dimensionality reduction, Principal Component Analysis, PCA, Kernel PCA, KPCA, Non-parametric regression, Curse of dimensionality, Nonlinearity.