## 5 Data and Experiments  
Our purpose in this paper is to solve a temporal regression problem for air quality modelling and prediction. We consider an air quality database that contains measurements of several parameters in the city of Wroclaw (Poland); in particular, we consider data from a communication station located within a wide street with two lanes in each direction (GPS coordinates: 51.086390 North, 17.012076 East; see Figure 2). One of the largest intersections in Wroclaw is located approximately 30 meters from the measuring station and is covered by traffic monitoring cameras. A weather measurement station is located on the outskirts of the city, at 9.6 km from the airport, and our data set is structured so that all such data are combined in an attempt to predict pollution concentrations. Pollution data are collected by the Provincial Environment Protection Inspectorate and encompasses the hourly NO\({}_{2}\) concentration values during three years, from 2015 to 2017. The traffic data are provided by the Traffic Public Transport Management Department of the Roads and City Maintenance Board in Wroclaw and include the hourly count of all types of vehicles passing the intersection. Public meteorological data are provided by the Institute of Meteorology and Water Management, and they include: air temperature, solar duration, wind speed, relative humidity, and air pressure. In order to make the data uniform, solar duration values were re-normalized in the real interval \([0,1]\). In the pre-processing phase, the instances with at least one missing value (617 samples, 2.3%) were deleted. Some basic statistic indicators on the remaining 25,687 instances are presented in Table 2.  
We considered, in particular, the set \(\mathcal{A}\) that contains the transport, meteorological, and pollution data from the year 2017. From it, we extracted the sets \(\mathcal{A}_{month}\), where _month_ranges from Jan to Dec, each containing the hourly data of the first 10 days of each month. Therefore, each \(\mathcal{A}_{month}\) contains exactly 240 instances. For each month, then, we designed a regression experiment using: (i) classic, non-temporal linear regression (using the class LinearRegression); (ii) classic, non-temporal decision tree regression (using the class RepTree); (iii) lagged linear regression on the lagged version of \(\mathcal{A}_{month}\), with \(l=10\); (iv) lagged propositional decision tree regression on the lagged version of \(\mathcal{A}_{month}\), with \(l=10\), and (v) feature and language selection for temporal decision tree regression on the transformed version of \(\mathcal{A}_{month}\), with \(l=10\) and \(\gamma=0.7\). We tested the prediction capabilities of each of the extracted models on the corresponding set \(\mathcal{A}_{month}\). In the case of temporal regression, each experiment returned a set of classifiers, more precisely a Pareto set; from it, we selected the classifier with the best correlation. All experiments were executed in 10-fold cross-validation mode, which guarantees the reliability of the results. Observe how different experiments correspond, in fact, to different preprocessing of the data: In (i) and (ii), a given \(\mathcal{A}_{month}\) contains 240 instances, each corresponding to a specific hour sample, and six (+1) columns, each corresponding to an independent variable (plus the dependent one). In (iii) and (iv), a given \(\mathcal{A}_{month}\) contains 60 (+1) columns, each being an independent variable or its lagged version, with lags from one to 10 h; therefore,