Climate dataset challenge

Your task is to answer these questions using appropriate linear models, and to produce elegant plots to communicate your findings. Please submit a Jupyter notebook, or a pdf. Include explanations of what your models are, and of what your plots show.

The dataset is from Code for retrieving the dataset is given at the bottom.

Fitting a linear model

To illustrate fitting a linear model (see section 2 of the course), we'll fit a simple periodic model: $$ Y_i \sim \alpha + \beta_1 \sin(2\pi t_i) + \beta_2 \cos(2\pi t_i) + \operatorname{Normal}(0,\sigma^2) $$

Plotting the residuals

Appendix: retrieving the dataset