Practical C

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Exercises

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The following packages are required for this practical:

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

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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?

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2. For each of the data sets elastic1 and elastic2, determine the regression of distance on 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?

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

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4. 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.

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

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

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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

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

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

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

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10. Inspect the diagnostic plots for the model obtained in exercise 12. What issues can you detect?

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End of Practical.