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Chapter 12: Q3E (page 722)

Short Answer

Expert verified

(A) We do not reject the null hypothesis, hence the value of 尾2=0

(B) We reject the null hypothesis at 95% significance level, thus, the value of 尾2=0

(C) Variable X2might not be related to dependent variable y even if mathematically 尾^2>尾^3

Step by step solution

01

Step-by-Step Solution Step 1: Testing the significance of β2

Therefore, value of尾2=0

02

Testing the significance of  β3

For, 伪=0.05the critical value of t0.025=2.042 using the formulae table is H0rejected if . t>t0.025Since, 3.2068 > 2.042, we reject the null hypothesis at 95% significance level.

Therefore, value of 尾3Is not equal to zero .

03

Predicting the model 

The null hypothesis H0;尾2=0 is not rejected while the null hypothesis H0:尾3=0 is rejected because the variableX2 might not have a relationship with Y . The hypothesis testing implies that variable X2 might not be predicting the overall model in a better way even if the mathematical value of coefficient of the variable calculated using the method of least square is higher than the other variable.

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Most popular questions from this chapter

Question: Suppose you fit the regression modelE(y)=尾0+尾1x1+尾2x2+尾3x1+尾4x12+尾5x22to n = 30 data points and wish to test H0: 尾3 = 尾4 = 尾5 = 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鈥檚 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 伪 = .05.

Question: Revenues of popular movies. The Internet Movie Database (www.imdb.com) monitors the gross revenues for all major motion pictures. The table on the next page gives both the domestic (United States and Canada) and international gross revenues for a sample of 25 popular movies.

  1. Write a first-order model for foreign gross revenues (y) as a function of domestic gross revenues (x).
  2. Write a second-order model for international gross revenues y as a function of domestic gross revenues x.
  3. Construct a scatterplot for these data. Which of the models from parts a and b appears to be the better choice for explaining the variation in foreign gross revenues?
  4. Fit the model of part b to the data and investigate its usefulness. Is there evidence of a curvilinear relationship between international and domestic gross revenues? Try using伪=0.05.
  5. Based on your analysis in part d, which of the models from parts a and b better explains the variation in international gross revenues? Compare your answer with your preliminary conclusion from part c.

Goal congruence in top management teams. Do chief executive officers (CEOs) and their top managers always agree on the goals of the company? Goal importance congruence between CEOs and vice presidents (VPs) was studied in the Academy of Management Journal (Feb. 2008). The researchers used regression to model a VP鈥檚 attitude toward the goal of improving efficiency (y) as a function of the two quantitative independent variables level of CEO (x1)leadership and level of congruence between the CEO and the VP (x2). A complete second-order model in x1and x2was fit to data collected for n = 517 top management team members at U.S. credit unions.

a. Write the complete second-order model for E(y).

b. The coefficient of determination for the model, part a, was reported asR2=0.14. Interpret this value.

c. The estimate of the尾-value for the(x2)2term in the model was found to be negative. Interpret this result, practically.

d. A t-test on the尾-value for the interaction term in the model,x1x2, resulted in a p-value of 0.02. Practically interpret this result, using伪=0.05.

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).

Reality TV and cosmetic surgery. Refer to the Body Image: An International Journal of Research (March 2010) study of the impact of reality TV shows on a college student鈥檚 decision to undergo cosmetic surgery, Exercise 12.17 (p. 725). Recall that the data for the study (simulated based on statistics reported in the journal article) are saved in the file. Consider the interaction model, , where y = desire to have cosmetic surgery (25-point scale), = {1 if male, 0 if female}, and = impression of reality TV (7-point scale). The model was fit to the data and the resulting SPSS printout appears below.

a.Give the least squares prediction equation.

b.Find the predicted level of desire (y) for a male college student with an impression-of-reality-TV-scale score of 5.

c.Conduct a test of overall model adequacy. Use a= 0.10.

d.Give a practical interpretation of R2a.

e.Give a practical interpretation of s.

f.Conduct a test (at a = 0.10) to determine if gender (x1) and impression of reality TV show (x4) interact in the prediction of level of desire for cosmetic surgery (y).
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