The director of a local tourist board is interested in determining the factors that influence the hotel occupancy rate in his city each month. Hotel occupancy can be measured as the percentage of available hotel rooms that are occupied by paying customers. He develops two models: Y = β 0 + β 1 X 1 + β 2 X 2 + β 3 X 3 + β 4 X 4 + ε and Y = β 0 + β 1 X 1 + β 2 X 2 + ε, where Y is the hotel occupancy rate (as a percentage), X 1 is the total number of passengers arriving at the airport (measured in thousands), X 2 is an average of local hotel room rates, X 3 is the consumer confidence index, and X 4 is a dummy variable = 1 during the months of June, July and August. He looks at data from the past 36 months and runs both of the regressions above. The results of these regressions are as follows:
Model 1: R 2 = 0.67 and SSE = 576, Model 2: R 2 = 0.61 and SSE = 733. Using the F - test on a subset of variables, test whether β 3 = β 4 = 0.

Question

The director of a local tourist board is interested in determining the factors that influence the hotel occupancy rate in his city each month. Hotel occupancy can be measured as the percentage of available hotel rooms that are occupied by paying customers. He develops two models:  Y  =  β 0   +  β 1 X 1   +  β 2 X 2   +  β 3 X 3   +  β 4 X 4   + ε and  Y  =  β 0   +  β 1 X 1   +  β 2 X 2   + ε, where  Y  is the hotel occupancy rate (as a percentage),  X 1   is the total number of passengers arriving at the airport (measured in thousands),  X 2   is an average of local hotel room rates,  X 3   is the consumer confidence index, and  X 4   is a dummy variable = 1 during the months of June, July and August. He looks at data from the past 36 months and runs both of the regressions above. The results of these regressions are as follows: 
 Model 1:  R 2   = 0.67 and  SSE  = 576, Model 2:  R 2   = 0.61 and  SSE  = 733. Using the  F - test on a subset of variables, test whether  β 3   =  β 4   = 0.

Answer

Since  F  = 4.22, we can reject  H 0   at α > 0.05. This means that at most one of  X 3 , the consumer confidence index, and  X 4 , the dummy variable that assumes a value of 1 during the months of June, July, and August, is statistically no significant indicator variable in explaining the hotel occupancy rate.

Answer

Since  F  = 3.12, we can reject  H 0   at α > 0.05. This means that at most one of  X 3 , the consumer confidence index, and  X 4 , the dummy variable that assumes a value of 1 during the months of June, July, and August, is statistically significant indicator variable in explaining the hotel occupancy rate.

Answer

Since  F  = 3.12, we can reject  H 0   at α > 0.05. This means that at least one of  X 3 , the consumer confidence index, and  X 4 , the dummy variable that assumes a value of 1 during the months of June, July, and August, is statistically significant indicator variable in explaining the hotel occupancy rate.

Answer

Since  F  = 4.22, we can reject  H 0   at α > 0.05. This means that at least one of  X 3 , the consumer confidence index, and  X 4 , the dummy variable that assumes a value of 1 during the months of June, July, and August, is statistically significant indicator variable in explaining the hotel occupancy rate.

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