5. For problem 4, import the data from https : Hraw . githubusercontent . com/hgveon2/s33859/master/hwl-datal . csv The imported dataset contains monthly sales (94 observations) for a bookstore. All data are in $100. (a) We want to regress sales on the time variables year and month. Check the scatterplot between sales and month, and comment on the monthly sales pattern. Then consider the following two models: model A - both year and month are used as numerical predictors model B - year is numerical but month is used as a categorical predictor. Fit models A and B and compare them in terms of adjusted R2. (1 pt) For the rest of the questions, use month as a categorical predictor. (b) Using model B, describe the yearly trend and the seasonal pattern. Use this model to predict the sales for the next 12 months. Discuss all model assumptions used in your predictions. (2 pt) (c) Check the model assumptions (model B). In particular, investigate whether adjacent residuals (lag 1) are correlated, using the DurbinWatson test. (1 pt) ((1) Assuming that the errors follow a rst-order autoregressive model, estimate the lag 1 autocorrelation ,0. Using this estimate, t another model (model C) that results in the best linear unbiased estimator of )3. Use the ACF plot to check whether the error independence assumption is met in this model. Compare model B and C in terms of A10. (3 pt)