NMIMS Solved Assignment Decision Science

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NMIMS Global Access

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.

 

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