Automobile Accidents. The file Accidents.xls contains information on 42,183 actual automobile accidents in 2001 in the United States that involved one of three levels of injury: NO INJURY, INJURY, or FATALITY. For each accident, additional information is recorded, such as day of week, weather conditions, and road type. A firm might be interested in developing a system for quickly classifying the severity of an accident based on initial reports and associated data in the system (some of which rely on GPS-assisted reporting).
Our goal here is to predict whether an accident just reported will involve an injury (MAX_SEV_IR = 1 or 2) or will not (MAX_SEV_IR = 0). For this purpose, create a dummy variable called INJURY that takes the value "yes" if MAX_SEV_IR = 1 or 2, and otherwise "no."
a. Using the information in this dataset, if an accident has just been reported and no further information is available, what should the
prediction be? (INJURY = Yes or No?) Why?
b. Select the first 12 records in the dataset and look only at the response (INJURY) and the two predictors WEATHER_R and TRAF_CON_R.
i. Create a pivot table that examines INJURY as a function of the 2 predictors for these 12 records. Use all 3 variables in the pivot table as rows/columns, and use counts for the cells.
ii. Compute the exact Bayes conditional probabilities of an injury (INJURY = Yes) given the six possible combinations of the predictors.
iii. Classify the 12 accidents using these probabilities and a cutoff of 0.5.
iv. Compute manually the naive Bayes conditional probability of an injury
given WEATHER_R = 1 and TRAF_CON_R = 1.
v. Run a naive Bayes classifier on the 12 records and 2 predictors using
XLMiner. Check detailed report to obtain probabilities and classifications
for all 12 records. Compare this to the exact Bayes classification. Are the
resulting classifications equivalent? Is the ranking (= ordering) of
observations equivalent?
c. Let us now return to the entire dataset. Partition the data into
training/validation sets (use XLMiner's "automatic" option for partitioning
percentages).
i. Assuming that no information or initial reports about the accident itself
are available at the time of prediction (only location characteristics,
weather conditions, etc.), which predictors can we include in the analysis?
(Use the Data_Codes sheet.)
ii. Run a naive Bayes classifier on the complete training set with the
relevant predictors (and INJURY as the response). Note that all predictors
are categorical. Show the classification matrix.
iii. What is the overall error for the validation set?
iv. What is the percent improvement relative to the naive rule (using the
validation set)?
v. Examine the conditional probabilities output. Why do we get a
probability of zero for P(INJURY = No | SPD_LIM = 5)?
Solution Preview :
In this paper, we analyzed the information on 42,183 actual automobile accidents in 2001 in the United States that involved one of three levels of injury : 1) NO INJURY, 2) INJURY, or 3) FATALITY. For each accident, additional information is recorded, such as day of week, weather conditions, and road type. We tried to classify the severity of an accident based on initial reports using Exact Bayes approach and Naive Bayes approach. We also compared the predictions from both the approaches.