Question 3 (10 marks)

The fileNutritionalStudy.xlsx(given in Moodle) contains information about the dietary intakes of fat and fibre on the cholesterol levels of 314 healthy adults.

a)Plot this data to show if there is any association between cholesterol levels and dietary fat intake and, separately, dietary fibre intake and describe the associations.

b)Based on these plots and their statistics, which dietary factor has the stronger influence on the cholesterol level? State the statistical feature/s that is the evidence for any statement.

c)Only for the stronger predictor of cholesterol level:

i)Does this dietary influence on cholesterol follow a linear relationship or not? Present and interpret an appropriate graph.

ii)Clearly interpret what the value of the slope indicates in this relationship.

iii) Calculate the residual when the dietary intake is 20.4g.

Average Fat Average Age Average Calorie Intake per Fibre Intake Cholesterol ID (years) Intake per clay day (9) per day (9) level (mgldL) 1 64 1298.8 57 6.3 170.3 2 76 1032.5 50.1 15.8 75.8 3 38 2372.3 83.6 19.1 257.9 4 40 2449.5 97.5 26.5 332.6 5 72 1952.1 82.6 16.2 170.8 6 40 1366.9 56 9.6 154.6 7 85 2213.9 52 28.7 255.1 8 58 1595.6 63.4 10.9 214.1 9 35 1800.5 57.8 20.3 233.6 10 55 1263.6 39.6 15.5 171.9 11 66 1460.8 58 18.2 137.4 12 40 1638.2 49.3 14.9 130.7 13 57 2072.9 106.7 9.6 420 14 66 987.5 35.6 10.3 254.9 15 66 1574.3 75 7.1 361.5 16 64 2868.5 128.8 15 379.5 17 62 1751.1 80.7 8.4 160.3 18 75 1407.6 35 20.8 144.1 19 68 1628.5 78.6 11.6 512.3 20 57 1101.4 48.5 8.5 197.2 21 56 2433.6 127.6 19.9 271.2 22 30 1437.3 61.5 8.8 160.9 23 34 2062.7 81.1 13.6 190.5 24 53 1276.5 50.1 9 143.5 25 60 2114.8 77.6 14.9 239.9 26 50 1113 32.8 12.9 104.8 27 62 1323 60.8 1 1.4 155.8 28 61 2837.3 84.2 33.8 192.1 29 65 2055.9 1 1 1 .8 15.9 226.5 30 71 1285.8 55.4 10.6 353.4 31 43 1786.9 93.9 10.6 247 32 33 3144.8 155 17.6 308.8 33 74 1241 53.1 10.8 206.1 34 41 2419.3 122.7 16.2 325.2 35 56 2712.7 145.3 13.4 242.6 36 44 1810 95.3 17.5 253.1 37 37 1778.1 75.9 10.8 332.6 38 37 1147.9 47.6 7.3 117 39 39 1951.4 109.1 4.7 461.1 40 37 2035.5 65.7 22.1 205.3 41 53 1248.6 56.9 8.2 223.2 42 66 3184.8 199 16.8 362.6