The paper discusses the moving least-squares (MLS) method for near-best approximations of functionals on R^d using scattered data. The method is based on the Backus-Gilbert approach and is shown to be effective for interpolation, smoothing, and derivative approximation. It is demonstrated that the MLS method provides near-best approximations, with local error bounded by the error of the best local polynomial approximation. The method produces a C^∞ function for interpolation in R^d and has an approximation order result for quasi-uniform data points. The MLS method is applied to univariate interpolation, smoothing, and derivative approximation, as well as to scattered-data interpolation in R^d (d=2,3). The method is shown to produce local approximations with small coefficient norms, leading to near-best approximation errors. The method is also extended to data-dependent approximations, where the penalty function is adapted based on the function's variation in different directions. The results show that the method provides accurate and smooth approximations, with the error bounded by a small factor times the error of the best local polynomial approximation. The method is tested on various examples, demonstrating its effectiveness in approximating functions with discontinuities and complex features. The results indicate that the MLS method is a powerful tool for scattered-data interpolation and approximation, providing near-best results with good locality and smoothness properties.The paper discusses the moving least-squares (MLS) method for near-best approximations of functionals on R^d using scattered data. The method is based on the Backus-Gilbert approach and is shown to be effective for interpolation, smoothing, and derivative approximation. It is demonstrated that the MLS method provides near-best approximations, with local error bounded by the error of the best local polynomial approximation. The method produces a C^∞ function for interpolation in R^d and has an approximation order result for quasi-uniform data points. The MLS method is applied to univariate interpolation, smoothing, and derivative approximation, as well as to scattered-data interpolation in R^d (d=2,3). The method is shown to produce local approximations with small coefficient norms, leading to near-best approximation errors. The method is also extended to data-dependent approximations, where the penalty function is adapted based on the function's variation in different directions. The results show that the method provides accurate and smooth approximations, with the error bounded by a small factor times the error of the best local polynomial approximation. The method is tested on various examples, demonstrating its effectiveness in approximating functions with discontinuities and complex features. The results indicate that the MLS method is a powerful tool for scattered-data interpolation and approximation, providing near-best results with good locality and smoothness properties.