Question

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, $\mathit{E}\mathbf{\left(}\mathit{Y}\mathbf{\right)}\mathbf{=}{\mathit{\beta }}_{\mathbf{0}}\mathbf{+}{\mathit{\beta }}_{\mathbf{1}}{\mathit{x}}_{\mathbf{1}}\mathbf{+}{\mathit{\beta }}_{\mathbf{2}}{\mathit{x}}_{\mathbf{4}}\mathbf{+}{\mathit{\beta }}_{\mathbf{3}}{\mathit{x}}_{\mathbf{1}}{\mathit{x}}_{\mathbf{4}}$, 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:$\hat{\mathbf{y}}=11.78-1.97x_1+0.58x_4-0.55x_1{x}_4$

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

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

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

$$\begin{gathered} \hat{\mathbf{y}}=11.78-1.97\left(0\right)+0.58x_4-0.55x_1{x}_4 \\ \hat{\mathbf{y}}=11.78+0.58x_4-0.55x_1{x}_4 \end{gathered}$$

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.

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

$$\begin{gathered} \hat{\mathbf{y}}=11.78-1.97\left(1\right)+0.58x_4-0.55x_1{x}_4 \\ \hat{\mathbf{y}}=11.78-1.97+0.58x_4-0.55x_1{x}_4 \\ \hat{\mathbf{y}}=9.81+0.58x_4-0.55x_1{x}_4 \end{gathered}$$

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.