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The appropriate test for examining the association between two categorical variables, like in this case (Diabetes in Family and Diabetes in Subject), is the Chi-squared test for independence.

The observed data is given as:

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	Diabetes in Subject: Yes	Diabetes in Subject: No	Total
Diabetes in Family: Yes	14	3	17
Diabetes in Family: No	3	50	53
Total	17

S. No.	Serum Creatinine	Weight	Gender
1	0.7	46	1
2	1.3	65	1
3	1	59	1
4	1.5	84	0
5	1.7	91	1
6	1.5	78	1
7	1	53	0
8	0.7	49	1
9	0.5	42	0
10	1.6	87	0
11	1.1	53	1
12	0.8	54	0
13	1.3	65	1
14	1.1	61	1
15	1.3	71	0
16	1.3	71	0
17	1.2	68	0
18	1.3	65	1
19	1	55	1
20	1.2	66	0
21	1.1	55	1
22	0.9	55	0
23	0.9	62	0
24	1.1	65	0
25	0.8	54	0
26	0.5	45	0
27	0.6	45	0
28	1	62	0
29	0.5	40	0
30	0.9	58	0
31	1.3	65	1
32	1.1	58	1
33	1.4	67	1
34	0.8	42	1
35	1.6	81	1
36	1.8	92	1
37	1.5	80	0
38	1.7	91	1
39	0.8	55	0
40	0.5	33	0

(i) Prepare a scatter plot to get an idea about the relationship among the variables.
(ii) Fit a linear regression model and its related analysis at 1% level of significance.
(iii) Does the fitted regression model satisfy the linearity and normality assumptions?
(iv) Also, draw both fitted regression lines on the scatter plot. 

A clinical study was conducted on individuals with advanced stage of Hepatocellular Carcinoma to test three lines of Treatments: T1, T2 and T3. Thirthy-six patients with stage III Hepatocellular Carcinoma who agreed to take part in the experiment were randomly allocated one of three line of Treatments T1, T2 and T3. The primary outcome was mortality, and patients were monitored for up to 60 months (5 years) after recruitment. The data (in months) so obtained are given as follows:  

Patient ID	Survival time	Outcome	Treatment	Patient ID	Survival time	Outcome	Treatment
ID001	14	Died	T3	ID019	50	Died	T1
ID002	27	Unknown	T1	ID020	54	Unknown	T3
ID003	37	Unknown	T3	ID021	57	Died	T2
ID004	44	Died	T1	ID022	60	Survived	T3
ID005	27	Died	T2	ID023	20	Died	T1
ID006	29	Died	T3	ID024	22	Unknown	T2
ID007	50	Died	T2	ID025	11	Unknown	T2
ID008	31	Died	T1	ID026	12	Unknown	T1
ID009	54	Died	T2	ID027	57	Unknown	T3
ID010	32	Died	T2	ID028	60	Survived	T3
ID011	32	Unknown	T2	ID029	44	Died	T1
ID012	60	Unknown	T1	ID030	47	Unknown	T2
ID013	2	Unknown	T2	ID031	32	Died	T2
ID014	42	Died	T3	ID032	34	Died	T1
ID015	42	Unknown	T2	ID033	17	Died	T2
ID016	60	Died	T3	ID034	6	Died	T1
ID017	60	Survived	T3	ID035	50	Unknown	T3
ID018	47	Died	T3	ID036	14	Unknown	T2

 For this data,
(i) Construct Kaplan and Meier survival curves.
(ii) Test whether there is a significant difference between the survival distributions of the patients under all treatments at 5% level of significance. 

A random sample of 440 patients of cardiology department of a hospital was taken and their workout timing and severity of heart disease status were recorded. The following table shows the workout timing and severity of heart disease:  

Workout (in minutes)		Severity of Heart Disease
		Low	Mild		Moderate		High			Very High
No workout		5	13		26		21			23
0- 15		6	15		19		19			21
15 to 30		16	17		14		16			12
30 to 45		18	17		13		11			9
45 to 60		20	19		15		13			7
≥ 60		16	22		6		5			6

 Test at 5% level of significance whether workout habit and heart disease are associated with to each other or not.  

To study the association between the diabetic patients and their family history of diabetes, the following data were obtained on 70 subjects.  

Diabetes in Family	Diabetes in Subject		Total
	Yes	No
Yes	14	3	17
No	3	50	53
Total	17	53	70

Which test is appropriate in this situation? Check whether the diabetes runs with generations in families or not at 5% level of significance using appropriate test.  

A hypothetical data of 40 patients on age (in years), weight (in kgs) and systolic blood pressure (in mm/hg) denoting 1 for high SBP and 0 for normal SBP are given in the following table:

S. No.	Age	Weight	SBP
1	52	60	0
2	56	68	1
3	51	54	0
4	63	74	1
5	54	62	0
6	51	67	0
7	51	66	0
8	54	65	0
9	59	71	1
10	51	89	1
11	56	72	1
12	55	72	1
13	46	57	0
14	42	54	0
15	52	63	0
16	65	67	1
17	50	67	0
18	42	53	0
19	50	68	1
20	39	55	0
21	47	48	0
22	42	45	0
23	45	57	0
24	56	83	1
25	49	63	0
26	56	94	1
27	55	87	1
28	53	67	0
29	65	70	1
30	44	70	0
31	48	54	0
32	61	79	1
33	45	85	0
34	63	98	1
35	49	78	0
36	65	80	1
37	60	70	1
38	53	98	1
39	41	53	0
40	50	70	1

For this data:

(i) Fit a multiple logistic regression model.

(ii) Test the significance of the individual model coefficients β₁ and β₂ at 5% level of significance.

(iii) Obtain the 95% confidence intervals for β₁ and β₂ .

(iv) Determine the Nagelkerke pseudo R-squared