An analyst studies quarterly data on the relationship between retail sales (y, i
ID: 3227454 • Letter: A
Question
An analyst studies quarterly data on the relationship between retail sales (y, in $ millions), gross national product (x, in $ billions), and a quarterly dummy d that equals 1 if the sales are for the 4th quarter; 0 otherwise. He estimates the model y = beta_0 + beta_1 x + beta_2 d + beta_3 xd + c. Relevant regression results are shown in the accompanying table. Interpret the dummy variable, d. At x = 0, predicted 4th quarter sales are greater than other quarters by about $112, 605.80 million. At x = 0, predicted 4th quarter sales are greater than other quarters by about $186, 553.30 million. At x = 0, predicted 4th quarter sales are greater than other quarters by about $299, 159.10 million. At x = 0, predicted 4th quarter sales are less than other quarters by about $186, 553.30 million. Is the dummy variable d significant at the 5% level? Yes, since we reject the relevant null hypothesis. Yes, since we do not reject the relevant null hypothesis. No, since we reject the relevant null hypothesis. No, since we do not reject the relevant null hypothesis. Interpret the interaction variable. Predicted increase in sales due to a $1 billion dollar increase in GNP is about $4.7 million lower in the 4th quarter than in other quarters. Predicted increase in sales due to a $1 billion dollar increase in GNP is about $4.7 million higher in the 4th quarter than in other quarters. Predicted increase in sales due to a $1 billion dollar increase in GNP is about $51.3 million lower in the 4th quarter than in other quarters. Predicted increase in sales due to a $1 billion dollar increase in GNP is about $51.3 million higher in the 4th quarter than in other quarters.Explanation / Answer
a-1) As the dummy variable has a positive coefficient of 112605.8, therefore we interpret it as: predicted 4th quarter sales ( when d =1 ) is greater than other quarters by about 112605.8.
Therefore a) is the correct answer here.
b-1) We see that the p-valeu for the dummy variable is 0.3424 > 0.05 that is the level of significance and therefore is is insignificant at the 5% level and the null hypothesis cannot be rejected.
Therefore d) is the correct answer here.
b-2) The coefficient of interaction term xd is -4.7, as it is negative therefore the predicted increase in sales due to a 1 billion dollar increase in GNP is about $4.7 million lower in the 4th quarter ( that is when d = 1) than in other quarters.
therefore a) is the correct answer here.