Chapter 12.3, Problem 12.17ACI

Reality TV and cosmetic surgery. How much influence does the media have on one’s decision to undergo-cosmetic surgery? This was the question of interest in Body Image: An International Journal of Research (March 201 0). In the study, 170 college students answered questions about their impressions of reality TV shows featuring cosmetic surgery. The five variables analyzed in the study were measured as follows:

DESIRE–scale ranging from 5 to 25, where the higher the value, the greater the interest in having cosmetic surgery

GENDER–1 if male, 0 if female

SELFESTM– scale ranging from 4 to 40, where the higher tile value, the greater the level of self-esteem

BODYSAT–scale ranging from 1 to 9, where the higher the value, the greater the satisfaction with one's own body

IMPREAL– scale ranging from 1 to 7, where the higher the value the more one believes reality television shows featuring cosmetic surgery are realistic

The data for the study (simulated based on statistics reported in the journal article) are saved in the file. Selected observations are listed in the accompanying table. Multiple regression was used to model desire to have cosmetic surgery (y) as a function of gender (x₁), self-esteem (x₂), body satisfaction (x₃ ), and impression of reality TV (x₄ ).

a.    Fit the first-order model, E (y) = β_{0 +} β₁ x_{1 +} β₂x_{2 +} β₃x_{3 +} β₄x₄, to the data in the file. Give the least squares prediction equation.

b.    Interpret the β estimates in the words of the problem.

c.    Is the overall model statistically useful for predicting desire to have cosmetic surgery? Test using α = .01.

d.    Which statistic. R² or $R_a^2$, is the preferred measure of model fit? Practically interpret the value of this statistic.

e.    Conduct a test to determine whether desire to have cosmetic surgery decreases linearly as level of body satisfaction increases. Use α = .05.

f.    Find a 95% confidence interval for β₄. Practically interpret the result.