In paulemms/datamining: Data mining

Introduction

This is Lab 11 on Data Mining. It describes how one can use interaction terms in linear regression.

First we load the datamining package and the data for the lab.

devtools::load_all()
load('crash-head.rda')

The data set

The variables in the data set are described in the table below.

| Variable | Description | | --- | --- | | Head | Head injury to the dummy | | D.P | Dummy in the Driver or Passenger seat | | Protection Kind of protection: | Driver and passenger airbags (d&p airbags) | Driver-side airbag (d airbag) | Motorized belts, Passive belts, Manual belts | Doors Number of doors on the car (2 or 4) | Size Car weight/size category: | small, light, compact, midsize, heavy, SUV

head(x)

The dataset is the result of crash tests on 274 cars, ranging over 1987-1992 model years. For each test, an instrumented dummy was seated in the car and the car was crashed into a barrier at 35mph.

The data is contained in variable x. All of the variables except Head are categorical. Head has already been transformed with a logarithm to make its distribution symmetric.

Historical context: Around this time period, automatic protection was required by law, but auto makers strongly preferred automatic belts over airbags, despite mounting evidence that automatic belts were ineffective and sometimes worse than manual belts. Congress took up the issue, and eventually ruled in 1991 that all new cars starting in 1998 must have driver and passenger airbags.

Linear model

1. Make a linear model to predict Head from all other variables. (Because Head is not the last column, you can’t use formula(x) this time.) Notice how 1m codes the categories. ?. Make a plot which shows the importance of Protection. Which protections make a difference to head injury (i.e. their effect is nonzero)? Which protections are significantly different from each other? Interactions
2. Find one significant interaction between D.P and the other variables. Add it to the model.
3. Repeat adding interactions with D.P until the residual plot is flat. ‘To verity that your interaction terms are useful, make a partial residual plot.
4. Now find and eliminate all interactions between Doors and the other variables, working one interaction at a time. Make a new partial residual plot.
5. Remove any irrelevant variables in the model. Make a summary of the final model for the homework.
6. You can now get checked off. Plotting residuals ‘To plot residuals or partial residuals using line charts: predict.plot (fit) predict.plot(fit,partial=T ,las=3) The option las=3 rotates the axis labels. Slice plots interact.plot (from lab 10) will make line charts when the predictors are categorical: interact .plot(fit) interact .plot(fit,ypred="D.P",1las=3) The second line makes only the plots with D.P as the slicing variable. Places where the curves fail to be flat are interactions. Adding interaction terms An interaction term between categorical variables is simply an indicator for a combination of categories. For example, suppose the head injury is unusually high for two-door SUVs. The interaction term for this would be Yes when Doors=2 and Size=SUV, and No otherwise. This term could be added to x as follows: xL,"door2.suv"] = factor.logical((xL,"Doors"]=="2") & (xL,"Size"]=="SUV")) Then re-fit the model including door2.suv. To later remove it from x: x = not(x,"door2.suv")

paulemms/datamining documentation built on March 1, 2023, 4:01 p.m.