# COVID-19's Pandemic Effects on Bike Sharing Systems: A New Reality for Urban Mobility?
## 3 Results
### Number of Rides Regression Model  
For the purpose of our analysis, daily data provided by the operator (Cyclopolis) of the BS systems were converted into weekly data, which were then used to construct an unbalanced panel dataset of the bike-sharing system in three Greek cities (Igoumenitsa, Rhodes, and Chania) from July 2019 to May 2020. To analyze the performance of bike-sharing systems we used as a dependent variable the number of rides recorded per week. This variable measures the level of usage of bike-sharing systems in each of the aforementioned Greek cities. In addition, we used a set of independent variables that can be associated with the number of rides. In many cases, the development of a model is highly affected and dependent on the attributes of the collected data. The model developed in the framework of the present research activity aimed to identify whether the lockdown period and the restriction measures applied affected the performance of the BS systems in three Greek cities which can be measured by how ridership was changed before, during, and after the lockdown. For this to be achieved, the number of rides, their duration, and whether the users returned the bicycles to the stations from which they rented them or not, based on the following assumptions, were used:  
* The duration could reveal if the users rented the bicycles for pleasure or (a) in order to move to/from their working locations and (b) other than the previous reasons. * The analysis of the data concerning the renting and returning stations of the bicycles was another factor that could reveal the purpose of using the bicycle as most likely the users that rented a bicycle for pleasure would return it to the same station; while the users renting it in order to move for other reasons would return to a station which is located nearest to their destination. Firstly, to control the effect of quarantine lockdown, we include a dummy variable that takes the value of 1 during the quarantine period, i.e., the weeks between 23 March and 4 May 2020 and zero otherwise. Moreover, we include an alternative dummy variable that takes the value of 1 during the quarantine period and beyond, i.e., all the weeks after 23 March 2020 and zero otherwise. We do so, in order to control whether the effect of quarantine lockdown on the performance of bike-sharing systems remains after the easing of restrictions on 4 May. Secondly, we include the average duration of the rides per week in each city. Finally, taking into account the availability of bike-sharing systems, the number of rental stations in each city is also included. Accordingly, the empirical model is formulated as follows:  
\[Y_{it}=b_{0}+b_{1}x_{1 it}+b_{2}x_{2 it}+b_{3}x_{3 it}+u_{it}with\ u_{it}=\gamma_{ i}+\varepsilon_{it}\]  
where,  
* \(x_{1 it}\): is the dummy for the general quarantine lockdown in Greece;
* \(x_{2 it}\): is the weekly average ride duration in each city;
* \(x_{3 it}\): is the number of rental stations;
* \(u_{it}\): is the composite error term;
* \(\gamma_{i}\): is a random effect, i.e., time-invariant characteristics of a city;
* \(\varepsilon_{it}\): is the error term;
* \(b_{0},\ b_{1},\ b_{2},\ b_{3}\): parameters to be estimated. In random-effects models, the random effect is a component of the composite error term, i.e., \(u_{it}=\gamma_{i}+\varepsilon_{it}\), and is not correlated with any regressor. Both random effect and errors are independently identically distributed, \(\gamma_{i}\sim IID\Big{(}0,\sigma_{\gamma}^{2}\Big{)}\) and \(\varepsilon_{it}\sim IID\big{(}0,\sigma_{\varepsilon}^{2}\big{)}\). Our random-effects model is estimated by ordinary least square (OLS) regressions with robust clustered standard errors in order to control for both heteroscedasticity and correlation of the error terms [36]. To decide between the use of fixed effects or random effects, we applied the standard Hausman test which showed that the appropriate specification is the random-effects model.