Dataset: Annual data from $2005$ to $2020$ for $100$ major European cities. The dataset includes variables such as air quality index $($AQI$),$ GDP per capita, population density, percentage of green spaces, and implementation of various environmental policies $($e$.$g$.,$ emission reduction programs, public transportation improvements, renewable energy incentives$).$ Use AQI as the dependent variable. Construct a panel data regression model to assess the impact of GDP per capita, population density, percentage of green spaces, and the implementation of environmental policies on air quality.

a$.$ How do you estimate and decide on the best model? Which one? the fixed effects or random effects models? Compare both models.

b$.$ What are the differences between panel data and time series data?