2. An observational study obtained decibel sound pressure level (SPL) data for an exponential horn (type of loudspeaker), as a function of distance from the audio source. The data is available in Canvas/Files/Data/_Exam 2 Data/spl.txt.
a. Prepare a comparative analysis of different regression models for this data. You should consider the linear model, and local (curvilinear) models, such as polynomial, spline and LOESS regression. Evaluate the model fits and provide your conclusion about which models best get at the data generating process. In your quantitative criteria be sure and include MAE and RMS error, as well as your recommendations for final model. Devise a tabular comparison to facilitate review of your models.
b. Unfortunately, the SPL sensor is subject to detecting random bursts of energy, resulting in occasional abnormally high readings. The data including these bad readings are in the file spl.contaminated.txt. Based on visual inspection, you would repeat your previous models and also include robust repression, such
as quantile regression (at least try the median), and Kendall-Theil regression. Be sure an provide pseudo R2 (one can use the nagelkerke function in the {rcompanion} package). Perform a complete analysis and comparison, make your conclusions and recommendation for the best model to use for this system.
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