Chapter 12: Q42E (page 739)

Question: Consumer behavior while waiting in line. The Journal of Consumer Research (November 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 0.25. 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.

Short Answer

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Answer

a) The interaction model equation for negative feelings score (y) to number of people ahead in line (x₁) and number behind in line (x₂) can be written as $y = β_{0} + β_{1} x_{1} + β_{2} x_{2} + β_{3} x_{1} x_{2}$ .

b) “x₁ and x₂ interact to affect y” means that number of people ahead in line (x₁) and number behind in line (x₂) are related to each other and collectively affect y. Changes in one variable affects the other and they collectively affect y.

c) β₃ in the model is not equal to zero and indicates that there is interaction amongst x₁and x₂.

d)“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” indicate that β₁ will have a positive sign as x₁ and y are positively related while β₂ will have a negative sign as x₂ and y are inversely related.

Step by step solution

Interaction model equation

The interaction model equation for negative feelings score (y) to number of people ahead in line (x₁) and number behind in line (x₂) can be written as $y = β_{0} + β_{1} x_{1} + β_{2} x_{2} + β_{3} x_{1} x_{2}$ .

Interaction term

“x₁ and x₂ interact to affect y” means that number of people ahead in line (x₁) and number behind in line (x₂) are related to each other and collectively affect y. Changes in one variable affects the other and they collectively affect y.

p-value interpretation

T-test for the interaction β in the model resulted in a p-value greater than 0.25. t-test H₀ is rejected when p-value < α. Here let us assume α of 0.05. since p-value > 0.025 is greater than 0.05, there is sufficient evidence to reject H₀.

Therefore, β₃ in the model is not equal to zero and indicates that there is interaction amongst x₁and x₂.

Signs of β

“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” indicate that β₁ will have a positive sign as x₁ and y are positively related while β₂ will have a negative sign as x₂ and y are inversely related.