The parametric methods such as a linear regression we have discussed in the previous week estimates the relationship between independent and dependent variables using their parameter. However, in a nonparametric regression such as the LOWESS function, we do estimate the regression function f(·) directly (Fox, 2002). In this discussion, we will be discussing the advantage and disadvantages of the LOWESS function which one of the nonparametric method also known as scatter plot smoothing technique. We will demonstrate the lowess function using R code and scatter plot.
Fox (2002) state LOWESS is one of the well-known nonparametric methods which is a locally weighted scatterplot smoother, for the simple-regression case. Marconi (2008) described the simplicity of lowess advantage is its biggest advantage as users are only need to specify the smoothing function as we have demonstrated in figure 1. The author state the disadvantage or drawback of using the LOWESS method is it does not produce any mathematical equation that will model the relationships between variables, unlike the parametric regression methods. Therefore, we could not reuse the a model from one dataset to another dataset directly and one has to apply LOWESS function every time for every new dataset. The author of the discussion post believes LOWESS is a great tool if the distribution of the dataset is unknown as we do not have any restrictions on whether our data follows normality or not. We will also be conducting a multi regression using R. When using the locally weighted scatterplot smoothing (LOWESS) method for multiple regression models in a k-nearest-neighbor-based model.
Fox, J. (2002). Nonparametric regression. Appendix to: An R and S-PLUS Companion to Applied Regression.
Marconi, D. (2008). New approaches to open problems in gene expression microarray data (Doctoral dissertation, alma).