Solve it using R

Data Table:

y1_TOT	y2_AMI	z1_GEN	z2_AMT	z3_PR	z4_DIAP	z5_QRS
3389	3149	1	7500	220	0	140
1101	653	1	1975	200	0	100
1131	810	0	3600	205	60	111
596	448	1	675	160	60	120
896	844	1	750	185	70	83
1767	1450	1	2500	180	60	80
807	493	1	350	154	80	98
1111	941	0	1500	200	70	93
645	547	1	375	137	60	105
628	392	1	1050	167	60	74
1360	1283	1	3000	180	60	80
652	458	1	450	160	64	60
860	722	1	1750	135	90	79
500	384	0	2000	160	60	80
781	501	0	4500	180	0	100
1070	405	0	1500	170	90	120
1754	1520	1	3000	180	0	129

7.25. Amitriptyline is prescribed by some physicians as an antidepressant. However, there are also conjectured side effects that seem to be related to the use of the drug: irregular heartbeat, abnormal blood pressures, and irregular waves on the electrocardiogram, among other things. Data gathered on 17 patients who were admitted to the hospital after an amitriptyline overdose are given in Table 7.6. The two response variables are Y1 = Total TCAD plasma level (TOT) Y2 = Amount of amitriptyline present in TCAD plasma level (AMI) The five predictor variables are Z1 = Gender: 1 if female, 0 if male (GEN) Z2 = Amount of antidepressants taken at time of overdose ( AMT) Z3 = PR wave measurement (PR) ZA = Diastolic blood pressure (DIAP) Zs = QRS wave measurement (QRS) Table 7.6 Amitriptyline Data Z1 Z2 23 Z4 TOT AMI GEN AMT PR DIAP QRS 3389 3149 7500 220 140 1101 653 1975 200 100 1131 810 HON, 3600 205 60 111 596 448 675 160 60 120 896 844 750 185 70 83 1767 1450 2500 180 60 80 807 493 350 154 80 98 1111 941 1500 200 70 93 645 547 375 137 60 105 628 392 1050 167 74 1360 1283 3000 180 60 80 652 458 450 160 64 860 722 1750 135 90 70 HOOOHHAHA 500 384 2000 160 60 80 781 501 4500 180 100 1070 405 1500 170 90 120 1754 1520 3000 180 0 129 Source: See [24]. (a) Perform a regression analysis using only the first response Y. (i) Suggest and fit appropriate linear regression models. (ii) Analyze the residuals. (iii) Construct a 95% prediction interval for Total TCAD for 21 = 1, z2 = 1200, Z3 = 140, z4 = 70, and 25 = 85. (b) Repeat Part a using the second response Y2. Exercises 427 (c) Perform a multivariate multiple regression analysis using both responses Y, and Y2. (i) Suggest and fit appropriate linear regression models. (ii) Analyze the residuals. (iii) Construct a 95% prediction ellipse for both Total TCAD and Amount of amitriptyline for 21 = 1, z2 = 1200, 23 = 140, 24 = 70, and zs = 85. Compare this ellipse with the prediction intervals in Parts a and b. Comment