(Situation M) Fast Food Chains Are Closely Watching What Proposed $t =$

Multiple Choice

(Situation M) Fast food chains are closely watching what proposed legislation will do to consumption of "huge meals" in the United States. Researchers have accumulated statistics on the annual consumption of "huge for the past 25 years. The goal of the analysis is to use the past data to predict future consumption and then compare the predicted consumption to the actual consumption in those years.
-Propose a straight-line model that includes both a long-term trend and a seasonal component for the time series. Let $t =$ the year in which the data was collected $( t = 1,2 , \ldots , 25 )$ and let $Q _ { 1 } , Q _ { 2 }$ , and $Q _ { 3 }$ be dummy variables used to model a seasonal effect.

A) $\mathrm { E } \left( \mathrm { Y } _ { \mathrm { t } } \right) = \beta _ { 0 } + \beta _ { 1 } \mathrm { Q } _ { 1 } + \beta _ { 3 } \mathrm { Q } _ { 2 } + \beta _ { 4 } \mathrm { Q } _ { 3 }$
B) $\mathrm { E } \left( \mathrm { Y } _ { \mathrm { t } } \right) = \beta _ { 1 \mathrm { t } }$
C) $\mathrm { E } \left( \mathrm { Y } _ { \mathrm { t } } \right) = \beta _ { 0 } + \beta _ { 1 } \mathrm { t } + \beta _ { 2 } \mathrm { Q } _ { 1 } + \beta _ { 3 } \mathrm { Q } _ { 2 } + \beta _ { 4 } \mathrm { Q } _ { 3 }$
D) $\mathrm { E } \left( \mathrm { Y } _ { \mathrm { t } } \right) = \beta _ { 0 } + \beta _ { 1 } \mathrm { t }$