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 2010). 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 the 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) = β0 + β1x1 + b2x2 + b3x3 + b4x4, to the data in the file. Give the least squares prediction equation.
b. Interpret the b 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 R2a, 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.

STUDENT DESIRE GENDER SELFESTM BODYSAT IMPREAL 24 3 11 13 11 11 18 4 4 2 3 20 25 22 166 167 168 169 170 18 13 25 26 13 20 27 3 5 6. 2 3 14 6. 3 0001 O..00 101