2) A medical researcher is studying percent body fat. As part of the study, the

Question

2) A medical researcher is studying percent body fat. As part of the study, the researcher takes data on 50 males aged 22 to 50. The dataset consists of the following variables: Fat% = percent body fat, Age = age (yrs), Weight = weight (lbs), Height = height (in.), Neck = neck circumference (cm), Chest = chest circumference (cm), Abdomen = abdomen circumference (cm), Hip = hip circumference (cm), Thigh = thigh circumference (cm). The data appear in the BodyFat2 worksheet of the HW8 data workbook on Moodle.

a) Use Excel to fit the multiple regression model using Weight as the dependent or Y variable and Height and Fat% as the independent or X variables. Is the model statistically significant at = 0.05?

b) Provide the equation of the fit line. Interpret the regression model parameters in the context of predicting weight.

c) Provide a point prediction for the weight of a male 70 inches tall with 20% body fat.

d) Provide an approximate 95% confidence interval for the average weight of males 70 inches tall with 20% body fat.

Obs Fat% Age Weight Height Neck Chest Abdomen Hip Thigh 1 12.6 23 154.25 67.75 36.2 93.1 85.2 94.5 59 2 6.9 22 173.25 72.25 38.5 93.6 83 98.7 58.7 3 24.6 22 154 66.25 34 95.8 87.9 99.2 59.6 4 10.9 26 184.75 72.25 37.4 101.8 86.4 101.2 60.1 5 27.8 24 184.25 71.25 34.4 97.3 100 101.9 63.2 6 20.6 24 210.25 74.75 39 104.5 94.4 107.8 66 7 19 26 181 69.75 36.4 105.1 90.7 100.3 58.4 8 12.8 25 176 72.5 37.8 99.6 88.5 97.1 60 9 5.1 25 191 74 38.1 100.9 82.5 99.9 62.9 10 12 23 198.25 73.5 42.1 99.6 88.6 104.1 63.1 11 7.5 26 186.25 74.5 38.5 101.5 83.6 98.2 59.7 12 8.5 27 216 76 39.4 103.6 90.9 107.7 66.2 13 20.5 32 180.5 69.5 38.4 102 91.6 103.9 63.4 14 20.8 30 205.25 71.25 39.4 104.1 101.8 108.6 66 15 21.7 35 187.75 69.5 40.5 101.3 96.4 100.1 69 16 20.5 35 162.75 66 36.4 99.1 92.8 99.2 63.1 17 28.1 34 195.75 71 38.9 101.9 96.4 105.2 64.8 18 22.4 32 209.25 71 42.1 107.6 97.5 107 66.9 19 16.1 28 183.75 67.75 38 106.8 89.6 102.4 64.2 20 16.5 33 211.75 73.5 40 106.2 100.5 109 65.8 21 19 28 179 68 39.1 103.3 95.9 104.9 63.5 22 15.3 28 200.5 69.75 41.3 111.4 98.8 104.8 63.4 23 15.7 31 140.25 68.25 33.9 86 76.4 94.6 57.4 24 17.6 32 148.75 70 35.5 86.7 80 93.4 54.9 25 14.2 28 151.25 67.75 34.5 90.2 76.3 95.8 58.4 26 4.6 27 159.25 71.5 35.7 89.6 79.7 96.5 55 27 8.5 34 131.5 67.5 36.2 88.6 74.6 85.3 51.7 28 22.4 31 148 67.5 38.8 97.4 88.7 94.7 57.5 29 4.7 27 133.25 64.75 36.4 93.5 73.9 88.5 50.1 30 9.4 29 160.75 69 36.7 97.4 83.5 98.7 58.9 31 12.3 32 182 73.75 38.7 100.5 88.7 99.8 57.5 32 6.5 29 160.25 71.25 37.3 93.5 84.5 100.6 58.5 33 13.4 27 168 71.25 38.1 93 79.1 94.5 57.3 34 20.9 41 218.5 71 39.8 111.7 100.5 108.3 67.1 35 31.1 41 247.25 73.5 42.1 117 115.6 116.1 71.2 36 38.2 49 191.75 65 38.4 118.5 113.1 113.8 61.9 37 23.6 40 202.25 70 38.5 106.5 100.9 106.2 63.5 38 27.5 50 196.75 68.25 42.1 105.6 98.8 104.8 66 39 33.8 46 363.15 72.25 51.2 136.2 148.1 147.7 87.3 40 31.3 50 203 67 40.2 114.8 108.1 102.5 61.3 41 33.1 45 262.75 68.75 43.2 128.3 126.2 125.6 72.5 42 31.7 44 205 69.5 36.6 106 104.3 115.5 70.6 43 30.4 48 217 70 37.3 113.3 111.2 114.1 67.7 44 30.8 41 212 71.5 41.5 106.6 104.3 106 65 45 8.4 39 125.25 68 31.5 85.1 76 88.2 50 46 14.1 43 164.25 73.25 35.7 96.6 81.5 97.2 58.4 47 11.2 40 133.5 67.5 33.6 88.2 73.7 88.5 53.3 48 6.4 39 148.5 71.25 34.6 89.8 79.5 92.7 52.7 49 13.4 45 135.75 68.5 32.8 92.3 83.4 90.4 52 50 5 47 127.5 66.75 34 83.4 70.4 87.2 50.6

Explanation / Answer

Summary statistics is as follows:

b.The equation of the fit line is given by:

-443.267 +3.10*Fat + 8.147*Height

c. Point prediction at Fat = 20 and height =70

=-443.267 + 3.10*20 +8.147*70 =189.023

d. We calculate the value at Lower 95% column and Upper 95% in the summary statistics at given pointand this is taken as interval

Confidence interval =

SUMMARY OUTPUT Regression Statistics Multiple R 0.810691214 R Square 0.657220244 Adjusted R Square 0.642633872 Standard Error 24.06614473 Observations 50 ANOVA df SS MS F Significance F Regression 2 52192.32866 26096.16433 45.05714091 1.18265E-11 Residual 47 27221.42814 579.1793222 Total 49 79413.7568 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -443.2676182 93.13704405 -4.759305201 1.88882E-05 -630.635183 -255.9000533 -630.635183 -255.9000533 Fat% 3.103859964 0.383778914 8.087625072 1.88545E-10 2.331796375 3.875923553 2.331796375 3.875923553 Height 8.146501599 1.307732618 6.229485667 1.20865E-07 5.515682911 10.77732029 5.515682911 10.77732029

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