NMIMS Solved Assignment Decision Science

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School for Continuing Education (NGA-SCE)

Course: Decision Science

Internal Assignment Applicable for September 2020 Examination

Assignment Marks: 30

 

The data set given in Table 1 is having variables namely, house price of unit area (Y), house age (X1), distance to nearest MRT station (X2), number of convenience stores (X3), latitude (X4), and longitude (X5).

Table 1: Data Set

Table Below

S.No.	X1	X2	X3	X4	X5	Y
1	6.4	90.45606	9	24.97433	121.5431	62.2
2	17.5	964.7496	4	24.98872	121.53411	38.2
3	12.7	170.1289	1	24.97371	121.52984	32.9
4	1.1	193.5845	6	24.96571	121.54089	54.4
5	0	208.3905	6	24.95618	121.53844	45.7
6	32.7	392.4459	6	24.96398	121.5425	30.5
7	0	292.9978	6	24.97744	121.54458	71
8	17.2	189.5181	8	24.97707	121.54308	47.1
9	12.2	1360.139	1	24.95204	121.54842	26.6
10	31.4	592.5006	2	24.9726	121.53561	34.1
11	4	2147.376	3	24.96299	121.51284	28.4
12	8.1	104.8101	5	24.96674	121.54067	51.6
13	33.3	196.6172	7	24.97701	121.54224	39.4
14	9.9	2102.427	3	24.96044	121.51462	23.1
15	14.8	393.2606	6	24.96172	121.53812	7.6
16	30.6	143.8383	8	24.98155	121.54142	53.3
17	20.6	737.9161	2	24.98092	121.54739	46.4
18	30.9	6396.283	1	24.94375	121.47883	12.2
19	13.6	4197.349	0	24.93885	121.50383	13
20	25.3	1583.722	3	24.96622	121.51709	30.6
21	16.6	289.3248	5	24.98203	121.54348	59.6
22	13.3	492.2313	5	24.96515	121.53737	31.3
23	13.6	492.2313	5	24.96515	121.53737	48
24	31.5	414.9476	4	24.98199	121.54464	32.5
25	0	185.4296	0	24.9711	121.5317	45.5
26	9.9	279.1726	7	24.97528	121.54541	57.4
27	1.1	193.5845	6	24.96571	121.54089	48.6
28	38.6	804.6897	4	24.97838	121.53477	62.9
29	3.8	383.8624	5	24.98085	121.54391	55
30	41.3	124.9912	6	24.96674	121.54039	60.7
31	38.5	216.8329	7	24.98086	121.54162	41
32	29.6	535.527	8	24.98092	121.53653	37.5
33	4	2147.376	3	24.96299	121.51284	30.7
34	26.6	482.7581	5	24.97433	121.53863	37.5
35	18	373.3937	8	24.9866	121.54082	39.5
36	33.4	186.9686	6	24.96604	121.54211	42.2
37	18.9	1009.235	0	24.96357	121.54951	20.8
38	11.4	390.5684	5	24.97937	121.54245	46.8
39	13.6	319.0708	6	24.96495	121.54277	47.4
40	10	942.4664	0	24.97843	121.52406	43.5
41	12.9	492.2313	5	24.96515	121.53737	42.5
42	16.2	289.3248	5	24.98203	121.54348	51.4
43	5.1	1559.827	3	24.97213	121.51627	28.9
44	19.8	640.6071	5	24.97017	121.54647	37.5
45	13.6	492.2313	5	24.96515	121.53737	40.1
46	11.9	1360.139	1	24.95204	121.54842	28.4
47	2.1	451.2438	5	24.97563	121.54694	45.5
48	0	185.4296	0	24.9711	121.5317	52.2
49	3.2	489.8821	8	24.97017	121.54494	43.2
50	16.4	3780.59	0	24.93293	121.51203	45.1
51	34.9	179.4538	8	24.97349	121.54245	39.7
52	35.8	170.7311	7	24.96719	121.54269	48.5
53	4.9	387.7721	9	24.98118	121.53788	44.7
54	12	1360.139	1	24.95204	121.54842	28.9
55	6.5	376.1709	6	24.95418	121.53713	40.9
56	16.9	4066.587	0	24.94297	121.50342	20.7
57	13.8	4082.015	0	24.94155	121.50381	15.6
58	30.7	1264.73	0	24.94883	121.52954	18.3
59	16.1	815.9314	4	24.97886	121.53464	35.6
60	11.6	390.5684	5	24.97937	121.54245	39.4
61	15.5	815.9314	4	24.97886	121.53464	37.4
62	3.5	49.66105	8	24.95836	121.53756	57.8
63	19.2	616.4004	3	24.97723	121.53767	39.6
64	16	4066.587	0	24.94297	121.50342	11.6
65	8.5	104.8101	5	24.96674	121.54067	55.5
66	0	185.4296	0	24.9711	121.5317	55.2
67	13.7	1236.564	1	24.97694	121.55391	30.6
68	0	292.9978	6	24.97744	121.54458	73.6
69	28.2	330.0854	8	24.97408	121.54011	43.4
70	27.6	515.1122	5	24.96299	121.5432	37.4
71	8.4	1962.628	1	24.95468	121.55481	23.5
72	24	4527.687	0	24.94741	121.49628	14.4
73	3.6	383.8624	5	24.98085	121.54391	58.8
74	6.6	90.45606	9	24.97433	121.5431	58.1
75	41.3	401.8807	4	24.98326	121.5446	35.1
76	4.3	432.0385	7	24.9805	121.53778	45.2
77	30.2	472.1745	3	24.97005	121.53758	36.5
78	13.9	4573.779	0	24.94867	121.49507	19.2
79	33	181.0766	9	24.97697	121.54262	42
80	13.1	1144.436	4	24.99176	121.53456	36.7
81	14	438.8513	1	24.97493	121.5273	42.6
82	26.9	4449.27	0	24.94898	121.49621	15.5
83	11.6	201.8939	8	24.98489	121.54121	55.9
84	13.5	2147.376	3	24.96299	121.51284	23.6
85	17	4082.015	0	24.94155	121.50381	18.8
86	14.1	2615.465	0	24.95495	121.56174	21.8
87	31.4	1447.286	3	24.97285	121.5173	21.5
88	20.9	2185.128	3	24.96322	121.51237	25.7
89	8.9	3078.176	0	24.95464	121.56627	22
90	34.8	190.0392	8	24.97707	121.54312	44.3
91	16.3	4066.587	0	24.94297	121.50342	20.5
92	35.3	616.5735	8	24.97945	121.53642	42.3
93	13.2	750.0704	2	24.97371	121.54951	37.8
94	43.8	57.58945	7	24.9675	121.54069	42.7
95	9.7	421.479	5	24.98246	121.54477	49.3
96	15.2	3771.895	0	24.93363	121.51158	29.3
97	15.2	461.1016	5	24.95425	121.5399	34.6
98	22.8	707.9067	2	24.981	121.54713	36.6
99	34.4	126.7286	8	24.96881	121.54089	48.2
100	34	157.6052	7	24.96628	121.54196	39.1

 

1. On the basis of data given in Table 1,

a. Compute the descriptive statistics using the box plot and comment upon the 5 point summary.

b. Construct the histogram for each of Xi’s as well as Y and comment upon the skewness.

c. Compute the standard deviation for X1, X2 and X3.

 

2. On the basis of data given in Table 1,

a. Draw the scatter plot of Y with each Xi (i = 1, 2, 3, 4, 5)

b. Find the correlation of Y with each Xi. Also check the significance of correlation coefficient at 5% level of significance for each

c. Using multiple regression, find the linear regression equation predicting Y on basis of Xi’s (i = 1, 2, 3, 4, 5) and comment upon R square and adjusted R square value.

d. If regression is showing any insignificant variable/s (subpart c), drop the variable/s from the regression equation and run the regression again. Now compare the R square and adjusted R square with the previous model and comment on the same.

 

3. Team leader Mr. X claims that the average output of his team is 900 pages per day. To check his claim 50 employees are selected at random and the average output is found at 854 pages with the standard deviation of 42 pages.

a. Construct the null hypothesis and alternate hypothesis for the given problem.

b. Is the claim of Mr. X true at 5% level of significance? Construct 95% confidence interval for the sample mean.