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Chapter 12: Q41E (page 739)

Question: Tilting in online poker. In poker, making bad decisions due to negative emotions is known as tilting. A study in the Journal of Gambling Studies (March, 2014) investigated the factors that affect the severity of tilting for online poker players. A survey of 214 online poker players produced data on the dependent variable, severity of tilting (y), measured on a 30-point scale (where higher values indicate a higher severity of tilting). Two independent variables measured were poker experience (x1, measured on a 30-point scale) and perceived effect of experience on tilting (x2, measured on a 28-point scale). The researchers fit the interaction model, . The results are shown below (p-values in parentheses).

  1. Evaluate the overall adequacy of the model using 伪 = .01.

b. The researchers hypothesize that the rate of change of severity of tilting (y) with perceived effect of experience on tilting (x2) depends on poker experience (x1). Do you agree? Test using 伪 = .01.

Short Answer

Expert verified

Answer

  1. At 95% confidence interval, it can be concluded that at least one of the parameters尾1,尾2,or尾3isnonzero.

b, At 95% confidence interval it is concluded that 尾3=0 Hence it can be concluded with enough evidence that x1and x2do not interact in the model.

Step by step solution

01

Overall adequacy of the model

To test the overall adequacy of the model, F-test is conducted

H0:尾1=尾2=尾3=0Ha:Atleastoneoftheparameters尾1,尾2,or尾3isnonzero

Here, F test statistic = SSEn-k+1=31.98

Value of F0.05,213,213 is 2.605

H0is rejected if F static >F0.05,213,213 for 伪=0.05,Since F >F0.05,213,213

Sufficient evidence to reject H0at 95% confidence interval

Thus,atleastoneoftheparameters尾1,尾2,or尾3isnonzero

02

 Step 2: Overall adequacy of the model

H0:尾3=0H0:尾3鈮�0

Here, t-test statistic = 尾^ss尾^s=-5.61

Value oft0.05,213 is 1.96

H0is rejected if t static > t0.05,24,24 .伪=0.05 since t < t0.05,24,24

Not sufficient evidence to reject H0at 95% confidence interval

Therefore, 尾3=0

Hence it can be concluded with enough evidence that x1 and x2 donot interact in the model

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Most popular questions from this chapter

Question: Job performance under time pressure. Time pressure is common at firms that must meet hard and fast deadlines. How do employees working in teams perform when they perceive time pressure? And, can this performance improve with a strong team leader? These were the research questions of interest in a study published in the Academy of Management Journal (October, 2015). Data were collected on n = 139 project teams working for a software company in India. Among the many variables recorded were team performance (y, measured on a 7-point scale), perceived time pressure (, measured on a 7-point scale), and whether or not the team had a strong and effective team leader (x2 = 1 if yes, 0 if no). The researchers hypothesized a curvilinear relationship between team performance (y) and perceived time pressure (), with different-shaped curves depending on whether or not the team had an effective leader (x2). A model for E(y) that supports this theory is the complete second-order model:E(y)=尾0+尾1x1+尾2x12+尾3x2+尾4x1x2+尾5x12x2

a. Write the equation for E(y) as a function of x1 when the team leader is not effective (x2= 0).

b. Write the equation for E(y) as a function ofwhen the team leader is effective (x2= 1).

c. The researchers reported the following b-estimates:.

尾0^=4.5,尾1^=0.13,尾3^=0.15,尾4^=0.15and尾5^=0.29Use these estimates to sketch the two equations, parts a and b. What is the nature of the curvilinear relationship when the team leaders is not effective? Effective?

Commercial refrigeration systems. The role of maintenance in energy saving in commercial refrigeration was the topic of an article in the Journal of Quality in Maintenance Engineering (Vol. 18, 2012). The authors provided the following illustration of data relating the efficiency (relative performance) of a refrigeration system to the fraction of total charges for cooling the system required for optimal performance. Based on the data shown in the graph (next page), hypothesize an appropriate model for relative performance (y) as a function of fraction of charge (x). What is the hypothesized sign (positive or negative) of the 尾2parameter in the model?

Question: Personality traits and job performance. Refer to the Journal of Applied Psychology (Jan. 2011) study of the relationship between task performance and conscientiousness, Exercise 12.54 (p. 747). Recall that the researchers used a quadratic model to relate y = task performance score (measured on a 30-point scale) to x1 = conscientiousness score (measured on a scale of -3 to +3). In addition, the researchers included job complexity in the model, where x2 = {1 if highly complex job, 0 if not}. The complete model took the form

E(y)=尾0+尾1x1+尾2x12+尾3x2+尾4x1x2+尾5x12x2herex2=1E(y)=尾0+尾1x1+尾2x12+尾3(1)+尾4x1(1)+尾5(1)2(1)E(y)=(尾0+尾3)+(尾1+尾4)x1+(尾2+尾5)(x1)2

a. For jobs that are not highly complex, write the equation of the model for E1y2 as a function of x1. (Substitute x2 = 0 into the equation.)

b. Refer to part a. What do each of the b鈥檚 represent in the model?

c. For highly complex jobs, write the equation of the model for E(y) as a function of x1. (Substitute x2 = 1 into the equation.)

d. Refer to part c. What do each of the b鈥檚 represent in the model?

e. Does the model support the researchers鈥� theory that the curvilinear relationship between task performance score (y) and conscientiousness score (x1) depends on job complexity (x2)? Explain.

Forecasting movie revenues with Twitter. Refer to the IEEE International Conference on Web Intelligence and Intelligent Agent Technology (2010) study on using the volume of chatter on Twitter.com to forecast movie box office revenue, Exercise 11.27 (p. 657). Recall that opening weekend box office revenue data (in millions of dollars) were collected for a sample of 24 recent movies. In addition to each movie鈥檚 tweet rate, i.e., the average number of tweets referring to the movie per hour 1 week prior to the movie鈥檚 release, the researchers also computed the ratio of positive to negative tweets (called the PN-ratio).

a) Give the equation of a first-order model relating revenue (y)to both tweet rate(x1)and PN-ratio(x2).

b) Which b in the model, part a, represents the change in revenue(y)for every 1-tweet increase in the tweet rate(x1), holding PN-ratio(x2)constant?

c) Which b in the model, part a, represents the change in revenue (y)for every 1-unit increase in the PN-ratio(x2), holding tweet rate(x1)constant?

d) The following coefficients were reported:R2=0.945andRa2=0.940. Give a practical interpretation for bothR2andRa2.

e) Conduct a test of the null hypothesis, H0;尾1=尾2=0. Use伪=0.05.

f) The researchers reported the p-values for testing,H0;尾1=0andH0;尾2=0 as both less than .0001. Interpret these results (use).

Question: Do blondes raise more funds? Refer to the Economic Letters (Vol. 100, 2008) study of whether the color of a female solicitor鈥檚 hair impacts the level of capital raised, Exercise 12.75 (p. 756). Recall that 955 households were contacted by a female solicitor to raise funds for hazard mitigation research. In addition to the household鈥檚 level of contribution (in dollars) and the hair color of the solicitor (blond Caucasian, brunette Caucasian, or minority female), the researcher also recorded the beauty rating of the solicitor (measured quantitatively, on a 10-point scale).

  1. Write a first-order model (with no interaction) for mean contribution level, E(y), as a function of a solicitor鈥檚 hair color and her beauty rating.
  2. Refer to the model, part a. For each hair color, express the change in contribution level for each 1-point increase in a solicitor鈥檚 beauty rating in terms of the model parameters.
  3. Write an interaction model for mean contribution level, E(y), as a function of a solicitor鈥檚 hair color and her beauty rating.
  4. Refer to the model, part c. For each hair color, express the change in contribution level for each 1-point increase in a solicitor鈥檚 beauty rating in terms of the model parameters.
  5. Refer to the model; part c. Illustrate the interaction with a graph.
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