Métodos bootstrap em regressão linear simples

Abstract

The act of establishing a linear mathematical equation (a line) that describes the relationship between two variables becomes fundamental in many situations, such as when two variables measure roughly the same thing, but one of them is relatively expensive, or hard to deal with, while the other doesn't. Another important issue that can be addressed using this relationship between two variables is to predict future values of one variable. In this context, a widely used traditional method is known as linear regression, which by minimizing the sum of the squares of the residuals, allows to determine estimates of the angular and linear coefficient of the sought line. In a linear regression analysis, the researcher is usually interested in making inferences about the model parameters, however, to do so requires assumptions that often cannot be assumed. Among the main assumptions we can mention the error distribution format of the model, which should be normal or also the existence of atypical data because in this case, the regression method gives a lot of weight to these data, which leads to a change in the orientation of the line. and distorting estimates, leading to errors in expected results. An alternative to traditional methods is the bootstrap resampling method, which makes inferences through replacement resamples obtained from the original sample. Without assuming assumptions, the bootstrap method allows quantifying uncertainty by calculating the standard errors and confidence intervals of unknown parameters. In linear regression studies two bootstrap methods can be considered: the pair bootstrap method and the residual bootstrap method. In this context, the objective of this work is to compare the confidence intervals of the parameters obtained with bootstrap methods with those obtained using the classical statistics. Using four data sets obtained in the literature, software R was used to perform regression line adjustments and to calculate confidence intervals. The results showed that bootstrap methods are a viable alternative to make inferences in regression models without the need to verify the assumptions.