While waiting in a long line for service (e.g., to use an ATM or at the post office), at some point you may decide to leave the queue. The Journal of Consumer Research (Nov. 2003) published a study of consumer behavior while waiting in a queue. A sample of n = 148 college students was asked to imagine that they were waiting in line at a post office to mail a package and that the estimated waiting time is 10 minutes or less. After a 10-minute wait, students were asked about their level of negative feelings (annoyed, anxious) on a scale of 1 (strongly disagree) to 9 (strongly agree). Before answering, however, the students were informed about how many people were ahead of them and behind them in the line. The researchers used regression to relate negative feelings score (y) to number ahead in line (x1) and number behind in line (x2).
a. The researchers fit an interaction model to the data. Write the hypothesized equation of this model.
b. In the words of the problem, explain what it means to say that "x1 and x2 interact to affect y."
c. A t-test for the interaction β in the model resulted in a p-value greater than .25. Interpret this result.
d. From their analysis, the researchers concluded that "the greater the number of people ahead, the higher the negative feeling score" and "the greater the number of people behind, the lower the negative feeling score." Use this information to determine the signs of β1 and β2 in the model.