How much influence does the media have on one’s decision to undergo cosmetic sur

Question

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. Using Excel, construct scatter plots for (y and x4), (y and x3), (y and x2). Attach your output from Excel. Please interpret the Pearson’s correlation coefficient described in each scatter plot.

b. Using excel, please estimate the unknown parameters (B1, B2,B3, and B4) and write the least square prediction equation. Attach output from Excel.

c. Interpret each parameter estimate (b0, b1, b2, b3, and b4) in English. d. is there sufficient evidence that the overall model is satisfactory for predicting desire to have cosmetic surgery? (test using =0.01). Please highlight in the attached excel file the appropriate F-value which assesses overall model fit.

e. Please conduct hypothesis test to determine whether desire to have cosmetic surgery decreases as the level of body satisfaction increases (=0.05). highlight in excel relevant information for this hypothesis. f. interpret the value of R 2 . g. 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. find estimate for the standard deviation of error term and interpret this value.

DESIRE GENDER SELFESTM BODYSAT IMPREAL 11 0 24 3 4 13 0 20 3 4 11 0 25 4 5 11 1 22 9 4 18 0 8 1 6 8 1 33 7 6 10 1 40 9 6 16 0 19 3 6 10 0 31 3 2 15 0 21 1 4 12 0 31 5 3 17 0 15 1 4 9 1 40 9 6 11 0 24 1 3 16 0 16 1 4 8 1 37 8 4 9 1 29 9 4 14 0 31 6 6 14 0 16 1 3 14 0 14 1 4 15 0 25 4 5 13 0 12 1 1 15 0 29 2 7 11 1 30 9 5 12 1 24 6 5 18 0 27 3 6 10 1 24 6 6 14 0 15 1 3 19 0 5 1 3 11 0 20 1 2 13 0 19 1 2 13 1 17 2 3 15 0 27 5 3 7 1 38 9 5 11 1 35 8 5 12 0 27 3 6 12 0 26 3 7 9 0 34 6 3 8 1 37 8 5 9 1 36 8 1 13 0 38 7 3 11 0 18 1 3 10 1 30 9 5 13 0 19 1 4 20 0 24 3 4 15 1 36 9 5 14 0 20 2 3 11 1 40 9 4 11 1 29 5 2 15 0 25 3 5 15 0 15 1 2 14 1 31 8 3 16 0 17 2 2 15 0 12 1 4 13 0 31 3 4 16 0 17 1 4 13 0 20 2 5 12 0 22 2 3 5 1 40 9 4 9 1 33 9 5 14 0 8 1 4 12 1 25 5 1 15 0 21 3 4 18 0 27 3 4 11 1 23 7 4 12 1 28 8 5 10 1 32 9 4 12 0 28 4 1 12 0 17 2 1 9 1 30 8 2 12 0 27 5 3 13 0 30 4 3 19 0 16 1 5 9 1 34 9 4 6 1 29 9 4 13 1 28 5 5 10 1 24 8 2 14 0 27 2 5 14 0 18 1 4 12 1 31 9 5 16 0 22 3 4 18 0 16 1 6 14 1 32 9 4 14 0 23 5 7 10 1 25 7 5 11 1 19 3 4 7 1 38 9 3 9 1 31 7 2 13 0 27 3 5 12 0 20 1 2 12 0 21 3 3 14 0 21 1 5 14 0 28 7 4 10 0 22 4 4 11 1 34 9 4 9 1 25 8 5 14 0 18 1 3 8 1 35 7 2 5 1 36 9 5 12 0 22 3 3 7 1 27 6 3 15 0 23 4 4 16 0 28 4 6 14 0 23 3 4 16 0 31 4 4 17 0 23 1 3 9 0 33 3 4 10 0 35 5 5 11 0 10 1 3 14 0 15 1 2 10 0 26 4 3 15 0 7 1 4 11 0 15 1 2 17 0 15 1 4 8 1 27 8 5 6 1 30 9 4 10 0 27 4 2 9 1 22 6 3 16 0 28 4 4 18 0 25 1 5 18 0 19 1 5 13 0 4 1 3 16 0 30 6 2 15 1 22 6 4 14 0 25 3 5 13 1 24 5 4 14 0 25 1 4 7 1 30 9 3 13 0 22 4 3 11 1 35 9 4 14 0 27 1 3 14 0 19 7 4 16 0 21 1 3 9 1 27 7 5 14 0 26 1 2 13 0 28 1 3 13 0 18 2 6 11 1 18 5 3 17 0 20 1 6 11 0 35 8 5 17 0 20 1 4 12 1 40 9 5 13 1 36 8 5 10 0 19 2 1 11 0 27 4 5 13 0 12 1 2 13 0 15 1 5 18 0 20 1 5 16 0 13 1 5 14 0 28 4 5 7 1 33 7 4 11 1 26 7 4 12 1 30 9 4 14 0 35 5 4 12 1 33 8 1 14 0 19 2 5 15 0 17 1 3 16 0 27 4 7 13 0 30 2 6 8 1 32 9 7 18 0 27 2 5 9 1 30 8 6 8 1 27 9 3 18 0 15 1 5 14 1 36 9 6 18 0 25 3 5 13 0 26 4 5 9 1 13 5 6 14 0 20 3 2 6 1 27 8 3

Explanation / Answer

b) go to data -> data analysis

select regression and select data

b1 = -2.186485

b2^ = +0.047941044

b3^ = -0.322331992 ,

b4^ = 0.493103102

c) beta coefficient is interpreted as if we increase dependent variable by 1 unit , then change in y will be bi units

for dummy variable like gender , the expected difference in male and female is b1

d) since significance F = 9.188-10^(-24) << 0.01

hence the overall model is significant

e)

t-stat =

p-value for 1-sided test = 0.02599799/2/2 = 0.013 < 0.05

hence we reject the null and conclude that the claim is right

f) R^2 =

this means that 49.755 % of variablity in y is explaiend by the model

g) when x1 =0 , x2 = 7 , x3 = 2 ,x4 = 5

y^ =

h) standard error =

Please rate my solution

SUMMARY OUTPUT Regression Statistics Multiple R 0.705378825 R Square 0.497559287 Adjusted R Square 0.485378906 Standard Error 2.250865082 Observations 170 ANOVA df SS MS F Significance F Regression 4 827.8332886 206.9583221 40.84923869 9.18861E-24 Residual 165 835.9549467 5.066393616 Total 169 1663.788235 Coefficients Standard Error t Stat P-value Lower 95% Intercept 14.01065899 0.775344345 18.07024078 5.87941E-41 12.47978374 GENDER -2.18648505 0.676629489 -3.231436236 0.001487052 -3.522453189 SELFESTM -0.047941044 0.036690663 -1.306627903 0.193157392 -0.120384763 BODYSAT -0.322331992 0.143481325 -2.24650833 0.02599799 -0.605628068 IMPREAL 0.493103102 0.127393292 3.870714813 0.000156056 0.241571974

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