Question

"Sex","Age","Weight","Dose","Heparin"
"Male",51,146.94,"High",-1.654
"Male",48,115.08,"High",1.489
"Male",65,83.54,"Low",1.757
"Male",44,94.94,"High",1.324
"Male",43,122.46,"High",-2.86
"Male",54,135.86,"Low",-3.55
"Male",44,116.91,"Low",-1.682
"Male",36,126.98,"High",-0.603
"Male",43,95.9,"High",1.58
"Male",55,127.79,"Low",-1.428
"Male",37,98.58,"High",1.345
"Male",53,121.99,"High",-0.58
"Male",46,74.96,"High",4.47
"Male",53,99.17,"High",0.674
"Male",46,78.35,"High",4.488
"Male",40,122.13,"High",-1.134
"Male",28,81.31,"High",2.617
"Male",37,134.13,"High",-1.895
"Male",39,84.23,"High",2.799
"Male",49,101.35,"Low",0.571
"Male",36,109.39,"Low",-0.41
"Male",48,90.31,"Low",1.116
"Male",40,108.31,"Low",-1.311
"Male",44,117.91,"High",-0.263
"Male",43,97.58,"Low",-1.211
"Male",42,116.8,"Low",-0.174
"Male",37,139.32,"Low",-3.19
"Male",41,108.24,"High",2.052
"Male",35,96.67,"High",0.653
"Male",37,162.38,"Low",-7.441
"Male",45,93.29,"High",1.58
"Male",38,100.41,"High",1.413
"Male",39,81.97,"Low",1.037
"Male",42,89.27,"Low",3.623
"Male",43,89.66,"High",1.49
"Male",40,158.19,"High",-4.324
"Male",37,118.59,"Low",-2.981
"Female",25,77.05,"High",3.94
"Female",38,120.97,"Low",0.666
"Female",42,83.59,"High",5.294
"Female",21,122.16,"Low",1.985
"Female",45,104.93,"High",3.339
"Female",42,70.12,"Low",3.86
"Female",44,92.88,"High",3.422
"Female",46,85.94,"Low",3.293
"Female",43,82.45,"High",4.074
"Female",45,95.56,"High",3.378
"Female",44,86.14,"Low",1.923
"Female",42,82.81,"High",3.494
"Female",51,142.11,"Low",-0.577
"Female",32,87.04,"Low",3.48
"Female",31,82.02,"High",4.136
"Female",59,100.19,"High",4.345
"Female",43,69.19,"High",7.576
"Female",34,106.71,"High",2.712
"Female",42,73.74,"High",3.608
"Female",57,115.93,"High",1.48
"Female",58,59.41,"High",6.555
"Female",43,96.76,"Low",2.277
"Female",39,106.94,"Low",2.377
"Female",43,100.03,"Low",2.377
"Female",35,113.35,"Low",0.049
"Female",39,84.42,"High",5.673
"Female",48,69.54,"Low",5.119
"Female",46,86.53,"High",3.85
"Female",40,123.97,"High",2.478
"Female",46,84.2,"High",2.878
"Female",41,91.71,"High",2.95
"Female",28,84.41,"High",3.88
"Female",45,107.26,"High",2.764
"Female",45,100.1,"High",2.806
"Female",49,80.98,"Low",4.686
"Female",51,94.32,"Low",1.479
"Female",43,91.91,"Low",1.756
"Female",37,91.22,"Low",1.803
"Female",49,68.84,"High",6.17
"Female",53,107.24,"Low",2.13
"Female",38,73.65,"High",4.419
"Female",43,71.33,"Low",3.795
"Female",35,89.46,"High",3.975
"Female",50,76.86,"High",4.472
"Female",40,91.56,"High",2.715
"Female",45,84.75,"Low",4.071
"Female",55,98.35,"Low",1.824
"Female",59,96.42,"Low",1.657
"Female",53,93.24,"High",5.398
"Female",67,124.64,"Low",-0.199
"Female",32,111.45,"High",3.857
"Female",52,76.56,"High",6.996
"Female",53,101.38,"High",4.104

The anticoagulant heparin is used for preventing blood clots of patients after surgery, and for the treat- ment and prevention of deep vein thrombosis. The most commonly used form of the drug requires careful monitoring, as misuse may leading to possible adverse outcomes. In a study concerning the effi- cacy of heparin, levels of the metabolite heparin sulphate in the blood of eligible volunteer patients were monitored.

The data file contains five columns:

• Sex: Sex of patient (Female or Male) ;
• Age: Age of patient (years);
• Weight: Weight of patient (kg);
• Dose: Initial dose of heparin received (Low or High);
• Heparin: Level of heparin sulphate in blood sample, measured 3 hours after dosing (relative scale).

Using these data, and multiple regression techniques, address the following questions (justifying your answers in each case):

(a) Does the Weight of the patient influence the level of heparin sulphate in the blood? If so, how?

(b) Does the Age of the patient influence the level of heparin sulphate in the blood? If so, how?

(c) On average, do Male patients have a lower or higher level of heparin sulphate in their bloodstream compared to Female patients of the same weight and age, when both are dosed initially with a High dose?

(d) Using the predict function in R, or otherwise, predict the level of heparin sulphate that would be detected in the blood of a 40 year old man, weighing 100 kg, who is dosed on the Low dose.

(e) Discuss how well, or how poorly, your chosen model fits the data, and how well the variation in the observed data is explained.

Answer 1

Correlation between variables using R -

Ans a:

Correlation between weight and Heparin = -0.84

Implies the variable weight highly influence the levels of Heparin in a patient.

The more the weight, the less will be the levels of Heparin on average

Ans b:

Correlation between Age and Heparin = 0.047

Implies the variable Age does not influence the levels of Heparin in a patient.

Ans c:

Pairs comparison for males with high dose

Pairs comparison for females with high dose

For a give weight and age with High dose, the average Heparin in males is 0.67 while in females it is 4.08

=> when dosed with high dose, males show less amount of Heparin than females for a particular age and weight

Ans d:

Using predict function, the value of Heparin for an 40 year old man with 100 kgs weight and low dosed is - "-0.08"