The Automobile dataset is from 1985 Ward's Automotive Yearbook and describing various attributes of different car make and models. Several of the attributes in the database could be used as a "class" attribute. Here we use price as the target (class) attribute. Load the Automobile dataset from UCI repository into a dataframe called cars.df. Encode num_of_doors, num-of-cylinders, engine-location and make to numerical representation using an appropriate encoding strategy. You can drop the other categorical variables.
Are there outliers in any one of the features in the data set? How do you identify outliers? Remove them but create a second data set with outliers removed called cars.no.df. Keep the original data set cars.df.
Using pairs.panel, what are the distributions of each of the features in the data set with outliers removed (cars.no.df)? Are they reasonably normal so you can apply a statistical learner such as regression? Can you normalize features through a log, inverse, or square-root transform? State which features should be transformed and then transform as needed and build a new data set, cars.tx.
What are the correlations to the response variable (price) for cars.no.df? Are there collinearities? Build a full correlation matrix.
Split each of the three data sets, cars.no.df, cars.df, and cars.tx 70%/30% so you retain 30% for testing using random sampling without replacement. Call the data sets, cars.training and cars.testing, cars.no.training and cars.no.testing, and cars.tx.training and cars.tx.testing.
Build three ideal multiple regression models for cars.training, cars.no.training, and cars.tx.training using backward elimination based on p-value for predicting price.
Build a Regression Tree model using rpart package for predicting price: one with cars.training, one with cars.no.training, and one with cars.tx.training.
Provide an analysis of all the 6 models (using their respective testing data sets), including Adjusted R-Squared and RMSE. Which of these models is the best? Why?
Using each of the regression models, how one unit change in highway-mpg translates into the price prediction? how about city-mpg? (do not apply backward feature elimination for only for this part).
For each of the predictions, calculate the 95% prediction interval for the price. (Exclude Regression Trees)