[Polovniautomobili] (http://www.polovniautomobili.com/) is the most popular website for selling new and used cars in Serbia. Next to its core functionality, it offers car tire search, registration price calculation, and others. Main idea of this project is to analyze car ads posted on the website, and predict the price of a car in relation to all the other cars posted on the website. The methods of machine learning used to achieve this are linear and ridge regression.
This project features two use cases:
- A web page
- A chrome extension
Using the web page, the user can enter the data related to the car he wishes to evaluate, and the system will predict a price, using the existing dataset. If the user disagrees with the calculated price, he can enter the price he thinks is more reasonable in a dialog that pops up. The data entered is then added to the dataset, and used in the next prediction in an effort to train the system and make it more accurate.
The project features a restful web service, which responds to requests sent by the chrome extension [CarPriceChrome] (https://github.com/dkeske/CarPriceChrome). After the user activates the extension in Chrome, upon opening a car ad on polovniautomobili.com, the extension will make a request to the service, and send the car's relevant data. The result (predicted price) is displayed next to the ad's title in bright orange.
The whole project is written in python 2.7.10 and Django 1.8.
Data is gathered using the website, and the API. Data is scraped using python library BeautifulSoup, processed, and only the important properties are being saved. All the data currently used is scraped off the website, and API usage is still in development.
Data is saved as a textual file in DataFiles/outputfilePolovni.txt and also in the sqlite3 database. Data model is located in models.py :
class carAd(models.Model):
- kw : car's engine output in kilowats
- km : total mileage in kilometres
- year : year of production
- ac : type of air (0 - manual, 1 - digital)
- gears : type of transmission (0 - manual, 1 - auto)
- body : type of body (hatchback, wagon, coupe, sedan; explained beneath)
- price : listed price
- idFromSite : unique id on the website
Currently the size of the dataset is 1075, but it is prone to change as the dataset is regularly updated. It usualy hovers around 1000 instances.
After gathering, cathegorical values are vectorized, and displayed as zeroes and ones. Features with more than two cathegorical values are displayed using a sparse matrix, or "dummy values". For example, car's body type, which can take one of the four different values, is transformed into 3 features (0-0-1; 0-1-0; 1-0-0), with all zeroes being the fourth one(0-0-0).
Generating training and testing set has an optional argument trainSize (method getSet() in DataFiles/load.py). If no value is provided, a training set containing 70 percent of the data is created, for purposes of analysis. If, on the other hand, the parameter is set to 1, the whole dataset will be used as training set, and no testing set will be created. The latter case is used when predicting a new car's value, using the whole dataset as training to improve accuracy.
Machine learning is implemented using the scikit-learn python library. Two classes are used, LinearRegression, and Ridge. Data is stored and procesed as numpy arrays.
Linear regression as a predictive model creates a relationship between a dependant variable, and one or more independent variables. In our case, car features make the independent variables, and the car price is the dependent one being predicted. Since we have more than one independent variable we are using multiple linear regression. The estimation method used is ordinary least squares (OLS), it is conceptually simple and computationally straightforward. The OLS method minimizes the sum of squared residuals.
Ridge regression is implemented using linear least squares with l2 regularization. This model solves a regression model where the loss function is the linear least squares function and regularization is given by the l2-norm. A parameter alpha is passed to the function, where small positive values of alpha improve the conditioning of the problem and reduce the variance of the estimates.
Training the prediction models generates an array of coefficients, which are then used to predict the car's price on the testing dataset. These coefficients indicate how much would a change of a certain parameter impact the price. Positive coefficients indicate that an increase in the parameter value would increase the car's price, and vice versa, the negative coefficient would yield a decrease.
Feature selection is currently based on domain specific knowledge and experience, and all the features are considered relevant.
Function coefficients generated by prediction models:
| Field | Linear | Ridge |
|---|---|---|
| kw | 4.21180144 | 4.04164517 |
| km | -0.00716541 | -0.00099128 |
| year | 498.83245088 | 477.62511538 |
| ac | 238.40808359 | 275.49430694 |
| gears | 140.40504664 | 182.91860709 |
| hatch | 41.13264686 | 17.13017652 |
| wagon | -108.02527716 | -196.97885862 |
| coupe | 1072.02449013 | 937.95758273 |
Example for field 'kw': Let's assume we have two identical cars, having all the same attributes but the power ('kw'). First one has 62kw, and the second one has 78. Since power has a positive coefficient, it's increase will increase the price. The difference (78-62=16) will increase the price by 16*4.21180144=67,3888 eur.
Results are very similar, with both methods varying slightly. Columns present results for the mean abs error, root mean squared error, and the coefficient of determination R^2 of the prediction.
| TABLE | Mean absolute error | Root mean squared error | How well does the model fit the data? 0-1 |
|---|---|---|---|
| LINEAR | 499.686262964 | 826.852566837 | 0.810947156567 |
| RIDGE | 489.43178462 | 733.111397862 | 0.843548547046 |
With the given dataset, ridge regression has proven to be a better solution, yielding a smaller absolute and root squared errors, and also better fitting the data.