The ordinary least squares bivariate regression is a widely used parametric technique for estimating a relationship between two variables. Based on the obtained regression model, it is possible to predict or forecast each variable by another. In order to obtain the best fitting, some assumptions about the analyzed data have to be met, e.g., homoscedasticity and a normality of the data distribution. When these assumptions are violated, the weighted regression is preferred. The objective of this paper is to present a new approach for determining of relevant weights, which can be used in the weighted least squares bivariate regression. The procedure for obtaining the proposed weights includes two steps. The first one is creating a sample of size n, which contains the medians of the slopes drawn through each pair (xi, yi) and the other pairs. The second step is based on n-times resampling of the sample of the medians by skipping a single median and estimating it by the others (n − 1) medians in the result sample. The proposed method is illustrated by two examples, which are based on Anscombe’s I and III datasets. The obtained regression equations are Y = 2.92576 + 0.50969.X and Y = 4.00563 + 0.34539.X, respectively for I and III datasets. The standard errors of the regression equations concerning the I dataset, obtained by the ordinary least squared regression and the proposed weighted approach are 1.237 and 0.944, respectively. The standard errors of the regression equations concerning the III dataset, obtained by the ordinary least squared regression and proposed weighted approach are 1.236 and 0.004, respectively. As a result, the coefficients of correlation between X and Y from the I dataset raised from 0.816 to 0.884 and from 0.816 to 1.000 for the III dataset data. Additional evidence for the better performance of the proposed variant over the classical one is the scissors apertures of the regression lines produced by the models Y = a + b.X and X = c + d.Y.