1. Why do we need to remove the variables with identical values before constructing regression models?

2. Consider the following linear regression model:1 fit1 - lm ( fmv ~ . - recordID , data = dat10kTrain )

(a). Formate a general linear hypothesis in matrix to test whether the dummy variablesof product type jointly affect the fair market value.

(b). Write a piece of R code to test the general linear hypothesis at the 1% significancelevel.

3. Write a piece of R code to fit a quadratic trend in time model by incorporatingthe January effect to the USD/CAD exchange rates. Does the model indicate thatthe January effect exists?

4. Write a piece of R code to calculate the forecasts and the 95% predictioninterval of the USD/CAD exchange rates with a random walk model for 22 days. Plotthe forecasts and the upper and lower bounds of the prediction interval together in onefigure. (Hint: use a wide range for y axis, otherwise, the bounds of the prediction intervalare not shown in the figure.)

5. Write an R function with signature calAC(y, k) to calculate the lag k autocorrelation for a time series y. What is the output of the following call1 calAC ( rates $Rate , 1)

6. Write R functions to calculate the mean percentage error, the mean square error, and the mean absolute percentage error. Based on these measures, which one ofthe following models performs the best: AR(1), AR(2), ARIMA(2, 0, 2)?