a) We can see that a lot of bikes have been rented during the holidays and during the weekends (workingday 1). Furthermore, for weather 3, the mean is significantly lower than for the other weather types, which is coherent with the fact that weather 3 is not a good weather to ride a bike. The trends for the number of bikes rented is therefore expected.
b) The results are expected. Indeed, it is logical that more bikes are rented when the temperature goes up, which is shown in the plot and with our positive a1 coefficient.
c) Season 1 is winter, season 2 is spring, season 3 is summer and season 4 is fall. The results in this table are then expected. Indeed, more bikes are rented in the summer than the rest of the year because usually the temperatures are higher and the weather is ideal to ride bikes. The number of bikes rented in the spring and in the fall is also pretty high because people enjoy being outdoors during these seasons. However, it is cold in the winter, so it is normal to see that the number of bikes rented dropped during this season.
d) We can see the number of bikes rented and the regression for each seasons here. The results are expected. Indeed, less bikes are rented in the winter because the weather is colder, but as the temperature goes up, more bikes are rented. In the summer, though, the coefficient a1 is negative because if the weather is too hot, people won't rent as many bikes. Furthermore, the number of bikes rented during the summer is high all season long, because it is the best season to ride bikes.
e) We know approximately how bikes will be rented based on the season, the day of the week and the temperature, thanks to the number and graphs from before. If we want to estimate how many rack spots to rent, we can estimate it thanks to the linear regression we have for each season. Indeed, based on the weather forecast and the predicted temperature, we can estimate the number of bikes rented through the linear regression, and rent rack spots accordingly.