In the following data, there is a vector miles , which describes US road traffic in total vehicle miles traveled per month between 2000 and 2014. If you look carefully at the data, you should see that there is a periodic component, with traffic peaking in summer and declining in winter. There is also a slow increase in overall traffic in the long term. We can describe this model as follows, where % indicates the modulo operator: yt = :%12 + [9121 \f1. Give an interpretation of this model. How does the first term impact the prediction at a given time t? What about the second term? What does it mean if I312 = 0? 2. Construct the design matrix X to set up the least squares problem X = y. Since = (g, . . . , n) and there are 180 data points in y, X should be a 180 X 13 matrix. Print the first 10 rows of X as output. 3. Compute the least-squares fit and write the i coefficients and the sum of squared prediction errors. Then plot the fitted line (the predictions given by j} = X ) on the same plot as the observed data y. Briefly comment on the relative values of the t%12 coefficients vs the u coefficient