A model to forecast quarterly sales (in $100,000s) has been estimated as follows: yt = 0.3t + 2Q1 + 0.8Q2 + 5, where Q1 is the dummy variable for quarter 1, Q2 is the dummy variable for quarter 2, and Q3 is the dummy variable for quarter 3. When all the three dummy variables are 0, we have quarter 4. Therefore quarter 4 is the baseline. (a) Assuming that the time series used starts at the 1st quarter of 2000 (where t=1) and ends at the 4th quarter of 2012, what would the forecast for the first and third quarter of 2015 be? Show computation.(b) What can be inferred from the fact that this forecasting model contains no coefficients for Quarter 3?

Assume that we have the following output after a specific iteration of the "step" function. What can we conclude? What will the "step" function do next?

Step: AIC=305.21

csat ~ area + metro + miles + percent + high + college

Df Sum of Sq RSS AIC

- high 1 851 21556 305.15

20705 308.21

- metro 1 3684 24390 311.07

- miles 1 4003 24708 311.70

- area 1 4415 25120 312.49

- college 1 6932 27638 317.08

- percent 1 123564 144269 396.40

Suppose that Xt follows an AR(2) process Xt = 0.6 + 0.2Xt1 0.01Xt2 + Wt

, where

Wt are i.i.d. N(0,1).

(a) What is the unconditional mean E(Xt).

(b) Compute V (Xt

|Ft1), where Ft1 represents all the information up to time t 1.