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Exercise

Modeling log-transformed monetary output

In this exercise, you will practice modeling on log-transformed monetary output, and then transforming the "log-money" predictions back into monetary units. The data loaded into your workspace records subjects' incomes in 2005 (Income2005), as well as the results of several aptitude tests taken by the subjects in 1981:

  • Arith
  • Word
  • Parag
  • Math
  • AFQT (Percentile on the Armed Forces Qualifying Test)

The data have already been split into training and test sets (income_train and income_test respectively) and are in the workspace. You will build a model of log(income) from the inputs, and then convert log(income) back into income.

Instructions
100 XP
  • Call summary() on income_train$Income2005 to see the summary statistics of income in the training set.
  • Write a formula to express log(Income2005) as a function of the five tests as the variable fmla.log. Print it.
  • Fit a linear model of log(Income2005) to the income_train data: model.log.
  • Use model.log to predict income on the income_test dataset. Put it in the column logpred.
    • Check summary() of logpred to see that the magnitudes are much different from those of Income2005.
  • Reverse the log transformation to put the predictions into "monetary units": exp(income_test$logpred).
    • Check summary() of pred.income and see that the magnitudes are now similar to Income2005 magnitudes.
  • Fill in the blanks to plot a scatter plot of predicted income vs income on the test set.