In this practical I detail multiple skills and show you a workflow for (predictive) analytics.

All the best,

Gerko

Exercises

The following packages are required for this practical:

library(dplyr)
library(magrittr)
library(mice)
library(ggplot2)
library(DAAG)
library(MASS)

Exercise 1

The data sets elastic1 and elastic2 from the package DAAG were obtained using the same apparatus, including the same rubber band, as the data frame elasticband.

  1. Using a different symbol and/or a different color, plot the data from the two data frames elastic1 and elastic2 on the same graph. Do the two sets of results appear consistent?

Exercise 2

  1. For each of the data sets elastic1 and elastic2, determine the regression of distance on stretch (i.e. model the outcome distance on the predictor stretch). In each case determine:
  • fitted values and standard errors of fitted values and
  • the \(R^2\) statistic.

Compare the two sets of results. What is the key difference between the two sets of data?

Exercise 3

  1. Study the residual vs leverage plots for both models. Hint use plot() on the fitted object

Because there is a single value that influences the estimation and is somewhat different than the other values, a robust form of regression may be advisable to obtain more stable estimates. When robust methods are used, we refrain from omitting a suspected outlier from our analysis. In general, with robust analysis, influential cases that are not conform the other cases receive less weight in the estimation procedure then under non-robust analysis.

Exercise 4

  1. Use the robust regression function rlm() from the MASS package to fit lines to the data in elastic1 and elastic2. Compare the results with those from use of lm():
  • residuals
  • regression coefficients,
  • standard errors of coefficients,
  • plots of residuals against fitted values.

Exercise 5

  1. Use the elastic2 variable stretch to obtain predictions on the model fitted on elastic1.

Exercise 6

  1. Now make a scatterplot to investigate similarity between plot the predicted values against the observed values for elastic2

The mammalsleep dataset is part of mice. It contains the Allison and Cicchetti (1976) data for mammalian species. To learn more about this data, type

?mammalsleep

Exercise 7

  1. Fit and inspect a model where brw is modeled from bw

Exercise 8

  1. Now fit and inspect a model where brw is predicted from both bw and species

Exercise 9

  1. Can you find a model that improves the \(R^2\) in modeling brw?

Exercise 10

  1. Inspect the diagnostic plots for the model obtained in exercise 16. What issues can you detect?

End of Practical.