Statistical Models and Methods
The Data
Data are available on the recommended prices of used cars in the United States. All cars are the same age, but have done different mileages and have different specifications. You have recently been employed by a used car dealership to build models to describe the dependence of recommended prices on potential explanatory variables, in order to use these models to price your own used cars. The data, which come in two parts, are available on Moodle. They are TrainData.txt Training data, which will be used to build models.
TestData.txt Test data, which will be used to assess predictions from the models built. They can be read into R (after saving the file in your working directory) using
Train = read.table("TrainData.txt",header = T)
Test = read.table("TestData.txt",header = T)
A description of the variables can be found in the file description.txt.
After reading in the data, you can look at the structure of the data (number of observa- tions/variable types etc) using the str() command, e.g. str(Train). For both data sets, you should treat the covariates Cylinder, Doors, Cruise, Sound and Leather as factors (they are treated as integers by default). This can be done using, for example,
Train$Cylinder = factor(Train$Cylinder)
The Task
(a) Using the TRAINING data, investigate models to explain the relationship between Price and the other variables. That is, Price (or transformations of it) is to be the response variable, and all other variables are potential explanatory variables.
(b) Use your fitted model(s) from (a) to predict the responses for the observations in the TEST data set. That is, for each of the observations in the Test data, use the values of the explanatory variables as input to your model(s) from (a) to obtain fitted/predicted responses for these observations. Compare your predicted responses with the known observed responses from the observations in the Test data, using suitable plots/numerical summaries.
Notes
- As with any analysis, the first step should be to do some exploratory analysis using any relevant plots and numerical summaries.
- For the model fitting, you can/should use any of the techniques we have covered this semester to investigate potential models. The task is deliberately open-ended, as would be the case in real situations working with real data. As this is a realistic situation with real data, there is not necessarily one single correct answer. Your job is to investigate potential models, and provide a summary of what they tell us about the problem we are trying to solve. The important point is that you correctly use the relevant techniques in a logical and principled manner, and provide a concise but insightful summary of your findings and reasoning. (Note however that you do not have to produce a report in a formal "report" format.)
- You should pay attention as to whether the model assumptions are being met, for example using suitable diagnostic plots, and consider any transformations of the numerical variables if appropriate. Also consider whether your conclusions depend on a few outlying or influential points.
- You should (briefly and concisely) interpret your model(s) and consider whether they make sense in the context of the problem, for example via interpreting the fitted parameters.
- You do not need to include all your R output, as you will generate lots of output when experimenting with the model fitting. However, you should include the output which is relevant to the arguments that you make when describing the logical developments of your model fitting, and any diagnostic plots which justify changes you make in order to meet the modelling assumptions. Finally, at all stages please remember to explain your reasoning and describe (concisely but accurately) the action you take and why, along with the relevant output.
Case Study: Visualising the data