Build a simple linear regression model to predict PSA level (Y) as a function of cancer volume (X) Use this model to predict the mean PSA level for a patient whose cancer volume is 20cc In addition to building the simple linear regression model, the focus of this discussion is to assess the degree to which the assumptions of homoscedasticity and normalityare satisfied ID PSA Level Cancer Vol Weight AGE BPH SVI CP Gleason Score 1 0 651 0 5599 15 959 50 0 0 0 6 2 0 852 0 3716 27 66 58 0 0 0 7 3 0 852 0 6005 14 732 74 0 0 0 7 4 0 852 0 3012 26 576 58 0 0 0 6 5 1 448 2 117 30 877 62 0 0 0 6 6 2 16 0 3499 25 28 50 0 0 0 6 7 2 16 2 0959 32 137 64 1 8589 0 0 6 8 2 34 1 9937 34 467 58 4 6646 0 0 6 9 2 858 0 4584 34 467 47 0 0 0 7 10 2 858 1 2461 25 534 63 0 0 0 6 11 3 561 1 284 36 598 65 0 0 0 6 12 3 561 0 2592 36 598 63 3 5609 0 0 6 13 3 561 5 0028 20 491 63 0 0 0 5488 7 14 3 857 4 3929 20 086 67 0 0 0 7 15 4 055 3 3535 31 187 57 0 0 0 6505 7 16 4 263 4 6646 21 328 66 0 0 0 6 17 4 349 0 657 33 784 70 3 4556 0 0 5488 7 18 4 437 9 8749 38 475 66 0 0 1 4477 6 19 4 759 0 5712 26 311 41 0 0 0 6 20 4 953 1 1972 46 063 70 5 2593 0 0 7 21 5 155 3 1582 30 569 59 0 0 0 6 22 5 259 7 846 33 115 60 4 3492 0 3 8574 7 23 5 474 0 5827 29 371 59 0 4493 0 0 6 24 5 529 5 9299 31 5 63 1 5527 0 3 2544 7 25 5 641 1 477 39 252 69 4 953 0 0 6 26 5 871 4 2631 22 646 68 1 3499 0 0 6 27 6 05 1 6653 41 264 65 0 0 0 4493 7 28 6 172 0 6703 47 942 67 6 1719 0 0 7 29 6 36 2 8292 22 874 67 1 2461 0 1 0513 7 30 6 619 11 134 29 371 65 0 0 5 0531 6 31 6 821 1 3364 59 74 65 7 0993 0 0 4493 6 32 7 463 1 1972 450 339 65 5 4739 0 0 6 33 7 463 3 5966 20 905 71 3 5609 0 0 6 34 7 538 1 0101 26 311 54 0 0 0 6 35 7 768 0 99 25 028 63 0 0 0 4493 6 36 8 085 3 7062 61 559 64 8 7583 0 0 7 37 8 671 4 1371 38 861 73 0 5599 0 5 2593 8 38 8 935 1 5841 10 697 64 0 0 0 7 39 9 116 14 2963 59 74 68 3 9354 1 6 2339 7 40 9 777 2 2255 20 287 56 2 56 0 0 8521 7 41 9 974 1 8589 23 104 60 0 0 0 8 42 10 074 4 2207 39 646 68 0 0 0 7 43 10 278 1 786 47 942 62 5 529 0 0 6505 6 44 10 697 5 8709 49 402 61 0 0 2 2479 7 45 12 429 4 4371 30 265 66 5 7546 0 0 6505 7 46 12 807 5 2593 29 666 61 1 8589 0 0 7 47 13 066 15 3329 54 598 79 6 5535 1 14 2963 8 48 13 066 3 1899 56 826 68 5 529 0 0 6505 7 49 13 33 5 7546 33 115 43 0 0 0 6 50 13 33 3 3872 35 517 70 3 9354 0 0 4493 6 51 14 296 2 9743 54 055 68 0 0 0 7 52 14 585 5 2593 68 717 64 7 9248 0 0 6 53 14 585 1 6653 37 713 64 4 4371 0 1 0513 7 54 14 732 8 4149 61 559 68 5 8709 0 4 2631 7 55 14 88 23 3361 33 784 59 0 0 0 8 56 15 18 3 5609 72 24 66 8 3311 0 0 7 57 16 281 2 6379 17 637 47 0 0 1 6487 7 58 16 281 1 5841 42 948 49 4 1371 0 0 6 59 16 61 1 716 65 366 70 1 5527 0 0 8 60 16 61 2 8864 46 993 61 3 6328 0 0 7 61 17 116 1 5841 91 836 73 10 2779 0 0 6 62 17 288 7 3891 41 264 63 5 0531 1 6 7531 7 63 17 288 16 119 33 784 72 0 0 4 7588 8 64 17 814 7 6141 50 4 66 7 4633 1 8 2482 7 65 17 814 7 9248 37 338 64 0 0 0 6 66 17 993 4 306 46 525 61 3 7434 0 0 6505 7 67 18 541 7 5383 48 424 68 5 9299 0 3 7434 7 68 19 298 9 025 57 397 72 10 0744 0 0 6505 7 69 19 298 0 6376 82 269 69 0 0 0 6 70 19 492 3 2871 119 104 72 10 2779 0 0 4493 7 71 20 287 6 4237 36 234 60 0 1 3 7434 7 72 20 905 3 1899 28 219 77 5 7546 0 0 7 73 21 328 3 3535 46 063 69 0 1 1 2461 7 74 21 758 6 2965 25 534 60 1 5527 1 3 2544 8 75 26 576 20 0855 46 993 69 0 1 6 7531 8 76 28 219 23 1039 26 05 68 0 9512 1 11 2459 6 77 29 666 7 4633 83 931 72 8 3311 0 1 6487 8 78 31 187 12 6797 77 478 78 10 2779 0 0 8 79 31 817 14 154 35 874 69 0 1 13 1971 7 80 33 448 16 119 45 604 63 0 0 1 4477 8 81 33 784 4 3492 21 542 66 1 7507 0 1 2461 7 82 34 124 12 3049 32 137 57 1 5527 0 10 2779 7 83 35 517 13 5991 48 911 77 0 5886 1 1 7507 7 84 35 517 14 5851 46 525 65 3 0649 0 5 7546 8 85 36 234 4 7588 40 854 60 5 4739 0 2 2479 8 86 37 713 27 1126 33 784 64 0 1 10 2779 8 87 39 646 7 5383 41 679 58 5 1552 0 0 6 88 40 854 5 6407 29 079 62 0 1 1 3499 7 89 53 517 16 6099 112 168 65 0 1 11 7048 8 90 54 055 4 7588 40 447 76 2 56 1 2 2479 8 91 56 261 25 7903 60 34 68 0 0 0 6 92 62 178 12 5535 39 646 61 3 8574 1 0 7 93 80 64 16 9455 48 424 68 0 1 3 7434 8 94 107 77 45 6042 49 402 44 0 1 8 7583 8 95 170 716 18 3568 29 964 52 0 1 11 7048 8 96 239 847 17 8143 43 38 68 4 7588 1 4 7588 8 97 265 072 32 1367 52 985 68 1 5527 1 18 1741

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Question: Build a simple linear regression model to predict PSA level (Y) as a function of cancer volume (X).Use this model to predict the mean PSA

Build a simple linear regression model to predict PSA level (Y) as a function of cancer volume (X).Use this model to predict the mean PSA level for a patient whose cancer volume is 20cc. In addition to building the simple linear regression model, the focus of this discussion is to assess the degree to which the assumptions of homoscedasticity and normalityare satisfied.

ID #	PSA Level	Cancer Vol.	Weight	AGE	BPH	SVI	CP	Gleason Score
1	0.651	0.5599	15.959	50	0	0	0	6
2	0.852	0.3716	27.66	58	0	0	0	7
3	0.852	0.6005	14.732	74	0	0	0	7
4	0.852	0.3012	26.576	58	0	0	0	6
5	1.448	2.117	30.877	62	0	0	0	6
6	2.16	0.3499	25.28	50	0	0	0	6
7	2.16	2.0959	32.137	64	1.8589	0	0	6
8	2.34	1.9937	34.467	58	4.6646	0	0	6
9	2.858	0.4584	34.467	47	0	0	0	7
10	2.858	1.2461	25.534	63	0	0	0	6
11	3.561	1.284	36.598	65	0	0	0	6
12	3.561	0.2592	36.598	63	3.5609	0	0	6
13	3.561	5.0028	20.491	63	0	0	0.5488	7
14	3.857	4.3929	20.086	67	0	0	0	7
15	4.055	3.3535	31.187	57	0	0	0.6505	7
16	4.263	4.6646	21.328	66	0	0	0	6
17	4.349	0.657	33.784	70	3.4556	0	0.5488	7
18	4.437	9.8749	38.475	66	0	0	1.4477	6
19	4.759	0.5712	26.311	41	0	0	0	6
20	4.953	1.1972	46.063	70	5.2593	0	0	7
21	5.155	3.1582	30.569	59	0	0	0	6
22	5.259	7.846	33.115	60	4.3492	0	3.8574	7
23	5.474	0.5827	29.371	59	0.4493	0	0	6
24	5.529	5.9299	31.5	63	1.5527	0	3.2544	7
25	5.641	1.477	39.252	69	4.953	0	0	6
26	5.871	4.2631	22.646	68	1.3499	0	0	6
27	6.05	1.6653	41.264	65	0	0	0.4493	7
28	6.172	0.6703	47.942	67	6.1719	0	0	7
29	6.36	2.8292	22.874	67	1.2461	0	1.0513	7
30	6.619	11.134	29.371	65	0	0	5.0531	6
31	6.821	1.3364	59.74	65	7.0993	0	0.4493	6
32	7.463	1.1972	450.339	65	5.4739	0	0	6
33	7.463	3.5966	20.905	71	3.5609	0	0	6
34	7.538	1.0101	26.311	54	0	0	0	6
35	7.768	0.99	25.028	63	0	0	0.4493	6
36	8.085	3.7062	61.559	64	8.7583	0	0	7
37	8.671	4.1371	38.861	73	0.5599	0	5.2593	8
38	8.935	1.5841	10.697	64	0	0	0	7
39	9.116	14.2963	59.74	68	3.9354	1	6.2339	7
40	9.777	2.2255	20.287	56	2.56	0	0.8521	7
41	9.974	1.8589	23.104	60	0	0	0	8
42	10.074	4.2207	39.646	68	0	0	0	7
43	10.278	1.786	47.942	62	5.529	0	0.6505	6
44	10.697	5.8709	49.402	61	0	0	2.2479	7
45	12.429	4.4371	30.265	66	5.7546	0	0.6505	7
46	12.807	5.2593	29.666	61	1.8589	0	0	7
47	13.066	15.3329	54.598	79	6.5535	1	14.2963	8
48	13.066	3.1899	56.826	68	5.529	0	0.6505	7
49	13.33	5.7546	33.115	43	0	0	0	6
50	13.33	3.3872	35.517	70	3.9354	0	0.4493	6
51	14.296	2.9743	54.055	68	0	0	0	7
52	14.585	5.2593	68.717	64	7.9248	0	0	6
53	14.585	1.6653	37.713	64	4.4371	0	1.0513	7
54	14.732	8.4149	61.559	68	5.8709	0	4.2631	7
55	14.88	23.3361	33.784	59	0	0	0	8
56	15.18	3.5609	72.24	66	8.3311	0	0	7
57	16.281	2.6379	17.637	47	0	0	1.6487	7
58	16.281	1.5841	42.948	49	4.1371	0	0	6
59	16.61	1.716	65.366	70	1.5527	0	0	8
60	16.61	2.8864	46.993	61	3.6328	0	0	7
61	17.116	1.5841	91.836	73	10.2779	0	0	6
62	17.288	7.3891	41.264	63	5.0531	1	6.7531	7
63	17.288	16.119	33.784	72	0	0	4.7588	8
64	17.814	7.6141	50.4	66	7.4633	1	8.2482	7
65	17.814	7.9248	37.338	64	0	0	0	6
66	17.993	4.306	46.525	61	3.7434	0	0.6505	7
67	18.541	7.5383	48.424	68	5.9299	0	3.7434	7
68	19.298	9.025	57.397	72	10.0744	0	0.6505	7
69	19.298	0.6376	82.269	69	0	0	0	6
70	19.492	3.2871	119.104	72	10.2779	0	0.4493	7
71	20.287	6.4237	36.234	60	0	1	3.7434	7
72	20.905	3.1899	28.219	77	5.7546	0	0	7
73	21.328	3.3535	46.063	69	0	1	1.2461	7
74	21.758	6.2965	25.534	60	1.5527	1	3.2544	8
75	26.576	20.0855	46.993	69	0	1	6.7531	8
76	28.219	23.1039	26.05	68	0.9512	1	11.2459	6
77	29.666	7.4633	83.931	72	8.3311	0	1.6487	8
78	31.187	12.6797	77.478	78	10.2779	0	0	8
79	31.817	14.154	35.874	69	0	1	13.1971	7
80	33.448	16.119	45.604	63	0	0	1.4477	8
81	33.784	4.3492	21.542	66	1.7507	0	1.2461	7
82	34.124	12.3049	32.137	57	1.5527	0	10.2779	7
83	35.517	13.5991	48.911	77	0.5886	1	1.7507	7
84	35.517	14.5851	46.525	65	3.0649	0	5.7546	8
85	36.234	4.7588	40.854	60	5.4739	0	2.2479	8
86	37.713	27.1126	33.784	64	0	1	10.2779	8
87	39.646	7.5383	41.679	58	5.1552	0	0	6
88	40.854	5.6407	29.079	62	0	1	1.3499	7
89	53.517	16.6099	112.168	65	0	1	11.7048	8
90	54.055	4.7588	40.447	76	2.56	1	2.2479	8
91	56.261	25.7903	60.34	68	0	0	0	6
92	62.178	12.5535	39.646	61	3.8574	1	0	7
93	80.64	16.9455	48.424	68	0	1	3.7434	8
94	107.77	45.6042	49.402	44	0	1	8.7583	8
95	170.716	18.3568	29.964	52	0	1	11.7048	8
96	239.847	17.8143	43.38	68	4.7588	1	4.7588	8
97	265.072	32.1367	52.985	68	1.5527	1	18.1741

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