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Chapter 12: Q.87E (page 766)

Question: 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’s decision to undergo cosmetic surgery, Exercise 12.43 (p. 739). The data saved in the file were used to fit the interaction model, E(Y)=β0+β1x1+β2x4+β3x1x4, where y = desire to have cosmetic surgery (25-point scale),x1= {1 if male, 0 if female}, and x4= impression of reality TV (7-point scale). From the SPSS printout (p. 739), the estimated equation is:y^=11.78-1.97x1+0.58x4-0.55x1x4

a. Give an estimate of the change in desire (y) for every 1-point increase in impression of reality TV show (x4) for female students.

b. Repeat part a for male students.

Short Answer

Expert verified

Answer

a. An estimate of the change in desire (y) for every 1-point increase in impression of reality TV show (x4)for female students is 0.58.

b. An estimate of the change in desire (y) for every 1-point increase in impression of reality TV show (x4)for male students is 0.58.

Step by step solution

01

Interpretation of coefficient of x1

The change in desire (y) for every 1-point increase in impression of reality TV show (x4) for female students will be measured when the value of x1= 0

y^=11.78-1.97(0)+0.58x4-0.55x1x4y^=11.78+0.58x4-0.55x1x4

An estimate of the change in desire (y) for every 1-point increase in impression of reality TV show () for female students is 0.58.

02

Evaluation of coefficient of x1

The change in desire (y) for every 1-point increase in impression of reality TV show () for male students will be measured when the value of = 1

y^=11.78-1.97(1)+0.58x4-0.55x1x4y^=11.78-1.97+0.58x4-0.55x1x4y^=9.81+0.58x4-0.55x1x4

An estimate of the change in desire (y) for every 1-point increase in impression of reality TV show (x4) for male students is 0.58.

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Most popular questions from this chapter

Question: Risk management performance. An article in the International Journal of Production Economics (Vol. 171, 2016) investigated the factors associated with a firm’s supply chain risk management performance (y). Five potential independent variables (all measured quantitatively) were considered: (1) firm size, (2) supplier orientation, (3) supplier dependency, (4) customer orientation, and (5) systemic purchasing. Consider running a stepwise regression to find the best subset of predictors for risk management performance.

a. How many 1-variable models are fit in step 1 of the stepwise regression?

b. Assume supplier orientation is selected in step 1. How many 2-variable models are fit in step 2 of the stepwise regression?

c. Assume systemic purchasing is selected in step 2. How many 3-variable models are fit in step 3 of the stepwise regression?

d. Assume customer orientation is selected in step 3. How many 4-variable models are fit in step 4 of the stepwise regression?

e. Through the first 4 steps of the stepwise regression, determine the total number of t-tests performed. Assuming each test uses an a = .05 level of significance, give an estimate of the probability of at least one Type I error in the stepwise regression.

Question:Suppose you fit the first-order model y=β0+β1x1+β2x2+β3x3+β4x4+β5x5+εto n=30 data points and obtain SSE = 0.33 and R2=0.92

(A) Do the values of SSE and R2suggest that the model provides a good fit to the data? Explain.

(B) Is the model of any use in predicting Y ? Test the null hypothesis H0:β1=β2=β3=β4=β5=0 against the alternative hypothesis {H}at least one of the parameters β1,β2,...,β5 is non zero.Useα=0.05 .

Question: Determine which pairs of the following models are “nested” models. For each pair of nested models, identify the complete and reduced model.

a.E(y)=β0+β1x1+β2x2b.E(y)=β0+β1x1c.E(y)=β0+β1x1+β2x12d.E(y)=β0+β1x1+β2x2+β3x1x2e.E(y)=β0+β1x1+β2x2+β3x1x2+β4x21+β5x22

Question: Write a regression model relating the mean value of y to a qualitative independent variable that can assume two levels. Interpret all the terms in the model.

Question: Do blondes raise more funds? Refer to the Economic Letters (Vol. 100, 2008) study of whether the color of a female solicitor’s 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’s 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’s 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’s 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’s 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’s 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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