(15 points) Reality TV and cosmetic surgery
(The data set for this assignment is posted on the 2ksb inside the folder files). How much influence does the media have on one’s decision to undergo cosmetic surgery? In the study, psychologists asked 170 college students about their impressions of reality TV shows featuring cosmetic surgeries. The psychologists used multiple regression 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. (2 points) Using SPSS, construct scatter plots for (y and x4), (y and x3), (y and x2). Attach your output from SPSS. Please interpret the Pearson’s correlation coefficient described in each scatter plot.
b. (2.5 points) Using SPSS, please estimate the unknown parameters (b1, b2,b3, and b4) and write the least square prediction equation. Attach output from SPSS.
c. (1.5 points) Interpret each parameter estimate (b0, b1, b2, b3, and b4) in English.
d. (2 points) is there sufficient evidence that the overall model is satisfactory for predicting desire to have cosmetic surgery? (test using α=0.01). Please highlight in the attached SPSS file the appropriate F-value which assesses overall model fit.
e. (2 points) Please conduct hypothesis test to determine whether desire to have cosmetic surgery decreases as the level of body satisfaction increases (α=0.05). highlight in SPSS relevant information for this hypothesis.
f. (1.5 points) interpret the value of R2.
g. (1.5 points) Please use the model developed in part (b) to estimate the desire to have cosmetic surgery when x1=0, x2=7, x3= 2, and x4=5.
h. (2 points) find estimate for the standard deviation of error term and interpret this value.
part a:
R-square is obtained from excel
correlation is the square root of R-square.
The sign of correlation (negative or positive) is based on the trend of slope in the graph (up or down).
part b:
the least square prediction equation is based on the intercept and the coefficients appearing inside the excel output.
part c:
for example, interpretation of coefficient b1 is phrased as how much increase or decrease there is in Y when X1 increase by 1 unit, while holding all the other variables constant.
part d:
it is a test of the entire regression model. The null hypothesis is that all the beta coefficients are simultaneously zero. The simple way to determine the test is to look inside the excel output for the significance F (p-value). if the significance F is below alpha (0.01) then the null hypothesis is rejected. Students are welcome to calculate critical F. Either way (p-value or critical F) is approved and will lead to same conclusion.
part e:
look at the p-value for b3. if the p-value is below 0.01 then the null hypothesis that beta3=0 is rejected. Students are welcome to calculate critical t. Either way (p-value or critical t) is approved and will lead to same conclusion.
part f:
R-square appears in the excel output. it is the amount of variance in the model explained by independent variables x1,x2, etc.
part g:
plug the values of x1,x2,etc into the regression equation in order to obtain estimated value of y.
part h:
calculate se/y (see example in the slide 62)
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