Plastic Hardness

Sixteen batches of plastic were made and from each batch one test item was molded. Each test item was randomly assigned to one of the four predetermined time levels, and the hardness was measured after the assigned elapsed time. The results are shown below with variables

library(tidyverse)
library(broom)
plastic <- tribble(~hardness, ~time,
                   199, 16,
                   205, 16,
                   196, 16,
                   200, 16,
                   218, 24,
                   220, 24,
                   215, 24,
                   223, 24,
                   237, 32,
                   234, 32,
                   235, 32,
                   230, 32,
                   250, 40,
                   248, 40,
                   253, 40,
                   246, 40)

  1. Make a residuals versus fits plot. Do you see any issues with the linear regression model?

  2. Is an F-test lack-of-fit appropriate here? If so, run an F-test lack of fit and state your conclusions.

  3. Make a normal probability plot. How does the normality assumption look?

Conceptual Exercises

  1. Suppose we reject the \(F\)-test lack-of-fit. Does that indicate what regression function is appropriate? How would you proceed?

Prostate Cancer

Refer to the Prostate Cancer dataset that you can download here: https://dcgerard.github.io/stat_415_615/data/prostate.csv

Build a regression model to predict PSA as a function of cancer volume. The analysis should include an assessment of the degree to which the key regression assumptions are satisfied. Include remedial measures where necessary. Provide an interpretation and describe measures of uncertainty in your analysis. Use best practices. Use the final model to predict the PSA for an individual with a cancer volume of 20 cc.