*12. How much influence does the media have on one's decision to undergo cosmetic surgery'? This was the question of interest in a study done by a journal dedicated to body image research. In the study, 170 college students answered questions about their impressions of reality TV shows featuring cosmetic surgery. The data for the study (simulated based on statistics reported in the journal articles) are given below. Multiple regression was used to model desire to have a cosmetic surgery (y) as a function of gender (x1) , self-esteem (x2) , body satisfaction (x3) , and impression of reality TV (x4) . Complete parts a through f. 1 Click the icon to view the data table. a. Fit the rst-order model, Ely) = Bo + [31x1 + [52x2 + [53x3 + 54x4, to the data. Give the least squares prediction equation. Em: +l )x1+()12+ (_)x3+ (_)X4 (Round to two decimal places as needed.) b. Interpret the [5 estimates in the words ofthe problem. Interpret the [30 estimate in the model. Choose the correct answer below. 0 A. The mean desire will increase by [30 for each additional in crease of1 unit of self-esteem, when all other variables are held constant. 0 B. The mean desire will decrease by Bo for each additional increase of 1 unit of impression of reality TV. when all other variables are held constant. 0 C. The mean desire is Bo units higher for males than females, when all other variables are being held constant. 0 D. It is the estimate of the ylnteroept. Interpret the [31 estimate in the model. Choose the correct answer below. 0 A. The mean desire is [31 units higher for males than females, when all other variables are being held constant. 0 B. It is the estimate of the yinteroept. O C. The mean desire will increase by [31 for each additional in crease of1 unit of body satisfaction, when all other variables are held constant. 0 D. The mean desire will increase by [3.1 for each additional in crease of1 unit of selfesteem, when all other variables are held constant. Interpret the [32 estimate in the model. Choose the correct answer below. 0 A. The mean desire is [32 units higher for males than females, when the variable self-esteem is held constant. 0 B. The mean desire will increase by [32 for each additional increase of1 unit of impression of reality TV, when all other variables are held constant O C. The mean desire will increase by B2 for each additional increase of 1 unit of self-esteem, when all other variables are held constant. O D. It is the estimate of the y-intercept. Interpret the By estimate in the model. Choose the correct answer below. O A. The mean desire will increase by By for each additional increase of 1 unit of impression of reality TV, when all other variables are held constant. O B. It is the estimate of the y-intercept. O C. The mean desire will increase by By for each additional increase of 1 unit of body satisfaction, when all other variables are held constant. O D. The mean desire is By units higher for males than females, when the variable body satisfaction is held constant. Interpret the B4 estimate in the model. Choose the correct answer below. O A. The mean desire is B4 units higher for males than females, when the variable impression of reality TV is held constant. O B. The mean desire will increase by B4 for each additional increase of 1 unit of impression of reality TV, when all other variables are held constant. O C. It is the estimate of the y-intercept. O D. The mean desire will decrease by B4 for each additional increase of 1 unit of body satisfaction, when all other variables are held constant. c. Test the adequacy of the model, using a = 0.05. Determine the null and alternative hypotheses. Choose the correct answer below. O A. Ho: B1 = B2 = B3 = B4 = 0. Ha: B1 # B2 # B3 # B4 # 0 O B. Ho: B1 = B2 = B3 = B4 =0, Ha: Exactly one Bj #0, i = 1, 2, 3, 4 O C. Ho: At least one B; $ 0, i= 1, 2, 3, 4, Ha: B1 = B2 = B3 = B4 =0 O D. Ho: B1 = B2 = B3 = B4 =0, Ha: At least one B, # 0, i=1, 2, 3, 4 The test statistic is F = (Round to two decimal places as needed.) The p-value is (Round to three decimal places as needed.) Since the p-value is (1). a = 0.05, (2) Ho. There (3) sufficient evidence to indicate at least one of the independent variables is useful in the prediction of the interest in having cosmetic surgery.d. Which statistic, R" or R is the preferred measure of model fit? Interpret the value of this statistic. The value of (4) % is the preferred measure of model fit, because it accounts for both the (5). and the number of (6) in the model. (Round to one decimal place as needed.) e. Conduct a test to determine whether desire to have cosmetic surgery decreases linearly as level of body satisfaction increases. Use a = 0.05. Determine the null and alternative hypotheses. Ho: (7) (8) 0 Ha: (9 ) (10) The test statistic is (Round to two decimal places as needed.) The p-value is (Round to three decimal places as needed.) Since the p-value is (11) a = 0.05, (12) Ho. There (13) sufficient evidence to indicate that cosmetic surgery decreases linearly as level of body satisfaction increases. f. Find a 95% confidence interval for B4. Interpret the result. The confidence interval is ( (Round to three decimal places as needed.) Interpret the result. Choose the correct answer below. O A. The confidence interval contains 95% of the possible values of the coefficient of a subject's belief that reality television shows featuring cosmetic surgery are realistic. O B. One can be 95% confident that the increase in mean desire for cosmetic surgery is between the lower and upper bounds of the confidence interval for each unit increase in impression of reality TV, holding all other variables constant. O C. The true value of the coefficient of a subject's belief that reality television shows featuring cosmetic surgery are realistic is within the upper and lower bound of the confidence interval. O D. The true value of the coefficient of a subject's belief that reality television shows featuring cosmetic surgery are realistic has a 95% probability of being within the confidence interval. 1: Data Table The five variables analyzed in the study were DESIRE-a measure where the higher the value, the greater the interest in having cosmetic surgery; GENDER-1 is male, 0 if female; SELFESTM-a measure where the higherthe value, the greater the level of self-esteem; BODYSAT-a measure where the higher the value, the greater the satisfaction with one's own body; IMPREAL-a measure where the higher the value, the more one believes reality television shows featuring cosmetic surgery are realistic. BODYSAT IMPREAL GENDER SELFESTM STUDENT DESIRE 24 11 20 13 25 11 22 11 18 33 TOUAWNOOO VOUAWN -0 0 0 - -6 -U1 - WWO V - 6 A W 16 14 14 20 14 -000- -0- 0600-0--606060- -00-06060--0-060 WW - UW ~ O U U W W N N WOODUU V - UA W O A A A W O A W A NO OOOAUAD 15 22 13 23 15 OWOON-A- 24 11 N 25 26 18 27 10 28 14 29 19 30 11 31 13 32 13 33 15 34 - NO CO O) W W OO OO UI N - - 35 36 12 37 12 38 39 40 oo - 41 13 18 4243 10 30 44 13 19 45 20 24 46 15 36 47 14 20 48 11 40 49 11 29 50 15 25 51 15 15 52 14 31 53 16 17 54 15 12 55 13 31 56 16 17 57 13 58 12 59 5 60 9 61 14 62 12 63 15 64 18 27 65 11 23 66 12 o--420-00-00---4000-00---00-0--000000-00--0-00- 28 ( NOW N U D - W O - N OUI O ( - A UIO N A D O V W W U - O O N N - W - N O - W U D NOW -DO UI N WAUNA OAUAUINUAA UW W N- - A U A AA - A UA W UAA A N W NUNA WUAAU 67 10 32 68 12 28 69 12 17 70 9 30 71 12 27 72 13 30 73 19 16 74 9 34 75 6 29 76 13 28 77 10 24 78 14 27 79 14 18 80 12 31 81 16 22 82 18 16 83 14 32 84 14 23 85 10 25 86 11 19 87 7 38 88 9 31 89 13 27JU 12 91 12 92 14 93 14 28 94 10 22 95 11 34 96 9 25 97 14 18 98 8 35 99 5 36 100 12 22 101 7 27 102 15 23 103 16 28 104 14 23 105 16 31 106 17 23 107 9 33 108 10 35 109 11 10 110 14 15 111 10 26 112 15 113 11 15 ooo - 060-0-0-0-06060-0- -060606060606-0- -0--06060 114 17 15 No - N - N - O AO - U WOD - - - 6 0 8 0 0 - - - 6 - - 0 W - A W A D O W Q - - O UA V- W- OWNUIWA WA W WAAVIANWOOD W NAYANA WN WOA WARSAW WONWOADDOWN 115 8 116 6 30 117 10 118 9 22 119 16 120 18 25 121 18 19 122 13 123 16 124 15 125 14 126 13 127 14 128 7 129 13 22 130 11 131 14 27 132 14 19 133 16 21 134 9 27 135 14 26 136 13 28 137 13 18138 11 139 17 140 11 35 141 17 142 12 143 13 144 10 145 11 146 13 WONNO 147 13 148 18 149 16 150 14 28 151 7 152 11 153 12 154 14 -0-00-0-40-0000-0--20000060--060- O WUD WO - O N O N D - N O UD ~ ~ A - - - - A N OO - 0 - U1 155 12 33 156 14 157 15 158 16 NNONTO 159 13 160 8 161 18 WNOUDOU WOUND TWO-AT 162 9 30 163 8 164 18 15 165 14 166 18 167 13 26 168 9 13 169 14 20 170 6 27 (1) O greater than or equal to (2) O fail to reject (3) O is not (4) O O less than O reject O is O (5) O variance (6) O B parameters (7) 0 B3 O P4 (8) O mean O dependent variables O Bo OOOO O sample size O degrees of freedom O B2 O B1(9) 0 B1 O Po (10) C = (11) O less than (12) O fail to reject O B2 > O greater than or equal to O reject OOOO O B4