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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

Expert verified

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 asy=β0+β1x1+β2x2+β3x1x2.

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 x1 ­and 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

01

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 asy=β0+β1x1+β2x2+β3x1x2.

02

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.

03

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 x1 ­and x2.

04

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.

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Most popular questions from this chapter

Question: Suppose you fit the regression modelE(y)=β0+β1x1+β2x2+β3x1+β4x12+β5x22to n = 30 data points and wish to test H0: β3 = β4 = β5 = 0

a. State the alternative hypothesis Ha.

b. Give the reduced model appropriate for conducting the test.

c. What are the numerator and denominator degrees of freedom associated with the F-statistic?

d. Suppose the SSE’s for the reduced and complete models are SSER = 1,250.2 and SSEC = 1,125.2. Conduct the hypothesis test and interpret the results of your test. Test using α = .05.


Factors that impact an auditor’s judgment. A study was conducted to determine the effects of linguistic delivery style and client credibility on auditors’ judgments (Advances in Accounting and Behavioural Research, 2004). Two hundred auditors from Big 5 accounting firms were each asked to perform an analytical review of a fictitious client’s financial statement. The researchers gave the auditors different information on the client’s credibility and linguistic delivery style of the client’s explanation. Each auditor then provided an assessment of the likelihood that the client-provided explanation accounted for the fluctuation in the financial statement. The three variables of interest—credibility (x1), linguistic delivery style (x2) , and likelihood (y) —were all measured on a numerical scale. Regression analysis was used to fit the interaction model,y=β0+β1x1+β2x2+β3x1x2+ε . The results are summarized in the table at the bottom of page.

a) Interpret the phrase client credibility and linguistic delivery style interact in the words of the problem.

b) Give the null and alternative hypotheses for testing the overall adequacy of the model.

c) Conduct the test, part b, using the information in the table.

d) Give the null and alternative hypotheses for testing whether client credibility and linguistic delivery style interact.

e) Conduct the test, part d, using the information in the table.

f) The researchers estimated the slope of the likelihood–linguistic delivery style line at a low level of client credibility 1x1 = 222. Obtain this estimate and interpret it in the words of the problem.

g) The researchers also estimated the slope of the likelihood–linguistic delivery style line at a high level of client credibility 1x1 = 462. Obtain this estimate and interpret it in the words of the problem.

Question: There are six independent variables, x1, x2, x3, x4, x5, and x6, that might be useful in predicting a response y. A total of n = 50 observations is available, and it is decided to employ stepwise regression to help in selecting the independent variables that appear to be useful. The software fits all possible one-variable models of the form

E(Y)=β0+β1xi

where xi is the ith independent variable, i = 1, 2, …, 6. The information in the table is provided from the computer printout.

a. Which independent variable is declared the best one variable predictor of y? Explain.

b. Would this variable be included in the model at this stage? Explain.

c. Describe the next phase that a stepwise procedure would execute.

Service workers and customer relations. A study in Industrial Marketing Management (February 2016) investigated the impact of service workers’ (e.g., waiters and waitresses) personal resources on the quality of the firm’s relationship with customers. The study focused on four types of personal resources: flexibility in dealing with customers(x1), service worker reputation(x2), empathy for the customer(x3), and service worker’s task alignment(x4). A multiple regression model was employed used to relate these four independent variables to relationship quality (y). Data were collected for n = 220 customers who had recent dealings with a service worker. (All variables were measured on a quantitative scale, based on responses to a questionnaire.)

a) Write a first-order model for E(y) as a function of the four independent variables. Refer to part

Which β coefficient measures the effect of flexibility(x1)on relationship quality (y), independently of the other

b) independent variables in the model?

c) Repeat part b for reputation(x2), empathy(x3), and task alignment(x4).

d) The researchers theorize that task alignment(x4)“moderates” the effect of each of the other x’s on relationship quality (y) — that is, the impact of eachx, x1,x2, orx3on y depends on(x4). Write an interaction model for E(y) that matches the researchers’ theory.

e) Refer to part d. What null hypothesis would you test to determine if the effect of flexibility(x1)on relationship quality (y) depends on task alignment(x4)?

f) Repeat part e for the effect of reputation(x2)and the effect of empathy(x3).

g) None of the t-tests for interaction were found to be “statistically significant”. Given these results, the researchers concluded that their theory was not supported. Do you agree?

Consider a multiple regression model for a response y, with one quantitative independent variable x1 and one qualitative variable at three levels.

a. Write a first-order model that relates the mean response E(y) to the quantitative independent variable.

b. Add the main effect terms for the qualitative independent variable to the model of part a. Specify the coding scheme you use.

c. Add terms to the model of part b to allow for interaction between the quantitative and qualitative independent variables.

d. Under what circumstances will the response lines of the model in part c be parallel?

e. Under what circumstances will the model in part c have only one response line?
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