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Task A: Downloading the data

Download the data for S&P 500 index, Boeing Stock Price, General Dynamics Corp. Stock Price, and US TN (10 Year)

Calculations

rt_S&P

rt_Boeng

rt_GD

S&P (x-xb)

Boeng(x-xb)

GD(x-xb)

 

0.00

0.00

0.00

-0.06

-1.02

-1.11

 

0.08

1.36

1.31

0.02

0.34

0.20

 

0.07

1.26

1.38

0.01

0.24

0.27

 

0.07

1.29

1.36

0.01

0.27

0.25

 

0.08

1.36

1.35

0.02

0.34

0.24

 

0.08

1.43

1.48

0.02

0.41

0.37

 

0.08

1.51

1.57

0.02

0.49

0.46

 

0.09

1.67

1.77

0.03

0.65

0.66

 

0.08

1.53

1.57

0.02

0.51

0.46

 

0.08

1.47

1.53

0.02

0.45

0.42

 

0.08

1.37

1.52

0.02

0.35

0.41

 

0.08

1.36

1.46

0.02

0.34

0.35

 

0.07

1.34

1.37

0.01

0.32

0.26

 

0.07

1.35

1.37

0.01

0.33

0.26

 

0.07

1.31

1.49

0.01

0.29

0.38

 

0.08

1.45

1.57

0.02

0.43

0.46

 

0.07

1.36

1.53

0.01

0.34

0.42

 

0.07

1.36

1.59

0.01

0.34

0.48

 

0.07

1.41

1.54

0.01

0.39

0.43

 

0.07

1.45

1.52

0.01

0.43

0.41

 

0.07

1.43

1.48

0.01

0.41

0.37

 

0.07

1.36

1.52

0.01

0.34

0.41

 

0.07

1.34

1.45

0.01

0.32

0.34

 

0.07

1.36

1.52

0.01

0.34

0.41

 

0.07

1.31

1.48

0.01

0.29

0.37

 

0.06

1.17

1.43

0.00

0.15

0.32

 

0.06

1.10

1.36

0.00

0.08

0.25

 

0.06

1.02

1.31

0.00

0.00

0.20

 

0.06

0.98

1.28

0.00

-0.04

0.17

 

0.06

0.96

1.18

0.00

-0.06

0.07

 

0.06

0.97

1.21

0.00

-0.05

0.10

 

0.06

0.85

1.15

0.00

-0.17

0.04

 

0.06

0.77

1.16

0.00

-0.25

0.05

 

0.06

0.75

1.10

0.00

-0.27

-0.01

 

0.05

0.74

1.05

-0.01

-0.28

-0.06

 

0.06

0.80

0.99

0.00

-0.22

-0.12

 

0.05

0.78

0.92

-0.01

-0.24

-0.19

 

0.05

0.80

0.92

-0.01

-0.22

-0.19

 

0.05

0.78

0.92

-0.01

-0.24

-0.19

 

0.05

0.74

0.85

-0.01

-0.28

-0.26

 

0.05

0.79

0.86

-0.01

-0.23

-0.25

 

0.05

0.83

0.86

-0.01

-0.19

-0.25

 

0.05

0.79

0.81

-0.01

-0.23

-0.30

 

0.05

0.79

0.79

-0.01

-0.23

-0.32

 

0.05

0.80

0.72

-0.01

-0.22

-0.39

 

0.05

0.75

0.69

-0.01

-0.27

-0.42

 

0.05

0.77

0.73

-0.01

-0.25

-0.38

 

0.05

0.69

0.75

-0.01

-0.33

-0.36

 

0.05

0.67

0.72

-0.01

-0.35

-0.39

 

0.05

0.67

0.74

-0.01

-0.35

-0.37

 

0.05

0.70

0.73

-0.01

-0.32

-0.38

 

0.05

0.71

0.72

-0.01

-0.31

-0.39

 

0.05

0.72

0.71

-0.01

-0.30

-0.40

 

0.05

0.70

0.67

-0.01

-0.32

-0.44

 

0.05

0.77

0.69

-0.01

-0.25

-0.42

 

0.05

0.77

0.73

-0.01

-0.25

-0.38

 

0.05

0.68

0.68

-0.01

-0.34

-0.43

 

0.05

0.69

0.69

-0.01

-0.33

-0.42

 

0.05

0.69

0.73

-0.01

-0.33

-0.38

 

0.05

0.84

0.75

-0.01

-0.18

-0.36

 

0.05

0.85

0.74

-0.01

-0.17

-0.37

 

0.05

0.79

0.76

-0.01

-0.23

-0.35

 

0.06

1.02

1.11

0.02

-0.16

0.02

Sum

0.01

0.31

0.34

 

 

 

 

62

62

62

JB test

 

 

 

 

 

K3

183.43933

-0.08719

0.007307

 

 

 

K4

15724.1905

-3.28337

-2.97871

 

 

JB

n[(K3)^2/6 + (k4)^2/24]

639077317

27.92822

22.9217

 

 

 

K3^2

33649.9879

0.007602

5.34E-05

 

 

 

K3^2/6

5608.33131

0.001267

8.9E-06

 

 

 

K4^2

247250168

10.78051

8.872705

 

 

 

K4^2/24

10302090.3

0.449188

0.369696

 

 

 

K3^2/6 + K4^2/24

10307698.7

0.450455

0.369705

 

 

JB

n[(K3)^2/6 + (k4)^2/24]

639077317

27.92822

22.9217

 

JB Test calculation

n[(K3)^2/6 + (k4)^2/24]

6.39E+08


33649.99

K3^2/6

5608.331

K4^2

2.47E+08

K4^2/24

10302090


10307699


6.39E+08

Null Hypothesis H0: The mean stock returns of GD is not equal to 2.8 percent

Alternate Hypothesis H1: The mean return of GD stock is equal to 2.8%

 

One-Sample Statistics

 

N

Mean

Std. Deviation

Std. Error Mean

rt_GD

62

1.1102

.37165

.04720

One-Sample Test

 

Test Value = 2.8                                    

 

t

Df

Sig. (2-tailed)

Mean Difference

95% Confidence Interval of the Difference

 

Lower

Upper

rt_GD

-35.802

61

.000

-1.68984

-1.7842

-1.5955








There exists mean difference of -1.68 for GD stock returns from t test statistics, t (61) = -35.8, 0.00<0.005 at 95% C.I. Hence, null hypothesis stating mean stock returns of GD is not equal to 0 is accepted

rt_Boeng

rt_GD

0

0

1.361862

1.31477

1.261369

1.382765

1.289841

1.356505

1.361862

1.351007

1.429208

1.478442

1.50696

1.572854

1.666428

1.773411

1.531658

1.570137

1.466517

1.52535

1.372705

1.517249

1.357241

1.456478

1.343204

1.37497

1.35375

1.37214

1.310635

1.492565

1.446994

1.574588

1.355034

1.52768

1.362233

1.588848

1.410461

1.538255

1.447203

1.523955

1.429821

1.479755

1.355402

1.515181

1.335847

1.454148

1.362976

1.519786

1.308919

1.482167

1.17166

1.428392

1.1

1.361306

1.015031

1.305502

0.980977

1.284869

0.95603

1.178703

0.966939

1.208474

0.854706

1.149174

0.769235

1.161049

0.747667

1.096983

0.735351

1.052088

0.801543

0.991973

0.778699

0.917101

0.800068

0.922346

0.778093

0.917859

0.742118

0.850201

0.789083

0.861703

0.833477

0.860072

0.79177

0.814668

0.78815

0.789956

0.803798

0.718084

0.747053

0.690324

0.772324

0.729291

0.690277

0.753526

0.665117

0.723174

0.668541

0.739484

0.700087

0.730891

0.714187

0.716028

0.723487

0.708268

0.696042

0.672905

0.768171

0.691231

0.766581

0.727541

0.677647

0.675313

0.689896

0.685122

0.694013

0.730677

0.835916

0.75036

Risk returns of Boeng and GD are computed and depicted in above table. F statistical testing was performed to observe differences
F-Test Two-Sample for Variances

F-Test Two-Sample for Variances




 

rt_Boeng

rt_GD

Mean

1.01746

1.110295

Variance

0.111919

0.138301

Observations

62

62

Df

61

61

F

0.809245


P(F<=f) one-tail

0.205428


F Critical one-tail

0.654094

 

F (61) = 0.80, F critical is greater than F statistics suggesting a slight mean variation between risk returns of the Boeng and GD stocks.


Correlation


 

rt_Boeng

rt_GD

rt_Boeng

1


rt_GD

0.952110318

1

So, we get r=0.95 which is based upon the correlation statistical testing which is just performed, since r value is positive and close to 1, it can be inferred that the risks associated with the Boeng and GD company stocks are same.

Regression Model

CAPM

SUMMARY OUTPUT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Regression Statistics

 

 

 

 

 

 

 

 

Multiple R

0.602263437

 

 

 

 

 

 

 

R Square

0.362721247

 

 

 

 

 

 

 

Adjusted R Square

0.352099934

 

 

 

 

 

 

 

Standard Error

0.507227183

 

 

 

 

 

 

 

Observations

62

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANOVA

 

 

 

 

 

 

 

 

 

df

SS

MS

F

Significance F

 

 

 

Regression

1

8.786175

8.786175

34.15032

2.24E-07

 

 

 

Residual

60

15.43676

0.257279

 

 

 

 

 

Total

61

24.22294

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

0.604712092

0.294961

2.05014

0.044728

0.014702

1.194723

0.014702

1.194723

xt_GD

-0.001012065

0.000173

-5.84383

2.24E-07

-0.00136

-0.00067

-0.00136

-0.00067

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RESIDUAL OUTPUT

 

 

 

 

PROBABILITY OUTPUT

 

 

 

 

 

 

 

 

 

 

 

 

Observation

Predicted Yt_GD

Residuals

Standard Residuals

 

Percentile

Yt_GD

 

 

1

0.604712092

-0.60471

-1.20209

 

0.806452

-2.13923

 

 

2

-0.735735938

-1.40349

-2.78996

 

2.419355

-1.97391

 

 

3

-0.774073496

-1.13916

-2.2645

 

4.032258

-1.91323

 

 

4

-0.755412526

-0.93808

-1.86478

 

5.645161

-1.80699

 

 

5

-0.73048338

-1.07651

-2.13996

 

7.258065

-1.80065

 

 

6

-0.701713067

-0.62484

-1.24211

 

8.870968

-1.7409

 

 

7

-0.6273589

-0.01779

-0.03536

 

10.48387

-1.73014

 

 

8

-0.538672197

0.388083

0.771456

 

12.09677

-1.71804

 

 

9

-0.662159101

0.057297

0.113898

 

13.70968

-1.69593

 

 

10

-0.655808446

0.113158

0.224944

 

15.32258

-1.6935

 

 

11

-0.666671778

0.312921

0.622045

 

16.93548

-1.67603

 

 

12

-0.722158779

0.379637

0.754666

 

18.54839

-1.6543

 

 

13

-0.776085718

0.174056

0.345999

 

20.16129

-1.64402

 

 

14

-0.819381229

-0.02448

-0.04866

 

21.77419

-1.62673

 

 

15

-0.80873752

0.386303

0.767917

 

23.3871

-1.61692

 

 

16

-0.719962769

0.71355

1.418442

 

25

-1.6068

 

 

17

-0.772511255

0.641191

1.274602

 

26.6129

-1.54053

 

 

18

-0.789870919

0.886719

1.762677

 

28.22581

-1.53832

 

 

19

-0.817411016

0.793666

1.577701

 

29.83871

-1.53288

 

 

20

-0.851875221

0.73883

1.468694

 

31.45161

-1.5321

 

 

21

-0.823038825

0.616794

1.226102

 

33.06452

-1.52833

 

 

22

-0.827182664

0.736363

1.46379

 

34.67742

-1.50877

 

 

23

-0.837333113

0.535481

1.064464

 

36.29032

-1.50368

 

 

24

-0.910093428

0.444879

0.88436

 

37.90323

-1.47569

 

 

25

-0.926918127

0.521085

1.035847

 

39.51613

-1.46583

 

 

26

-0.982224601

0.558616

1.110453

 

41.12903

-1.44071

 

 

27

-1.01101954

0.697326

1.386189

 

42.74194

-1.4143

 

 

28

-1.04467578

0.186177

0.370095

 

44.35484

-1.38095

 

 

29

-1.019955171

-0.17318

-0.34425

 

45.96774

-1.37897

 

 

30

-1.100388947

-0.31391

-0.62401

 

47.58065

-1.33246

 

 

31

-1.046981339

-0.49354

-0.9811

 

49.19355

-1.32656

 

 

32

-1.096261131

-0.36957

-0.73465

 

50.80645

-1.31511

 

 

33

-1.172242391

-0.20871

-0.41488

 

52.41935

-1.27883

 

 

34

-1.22212869

-0.42189

-0.83866

 

54.03226

-1.19452

 

 

35

-1.265204452

-0.70871

-1.40882

 

55.64516

-1.19313

 

 

36

-1.198573916

-0.47745

-0.94911

 

57.25806

-1.18064

 

 

37

-1.27638435

-0.46451

-0.92339

 

58.87097

-1.02188

 

 

38

-1.289408258

-0.51125

-1.01629

 

60.48387

-1.00346

 

 

39

-1.30118056

-0.42896

-0.85272

 

62.09677

-0.92147

 

 

40

-1.341314986

-0.26548

-0.52775

 

63.70968

-0.8585

 

 

41

-1.378369798

-0.27593

-0.54851

 

65.32258

-0.84386

 

 

42

-1.348408287

-0.34752

-0.69082

 

66.93548

-0.64515

 

 

43

-1.422027586

-0.1063

-0.21132

 

68.54839

-0.60486

 

 

44

-1.390576308

-0.32747

-0.65096

 

70.16129

-0.60203

 

 

45

-1.436872584

-0.18004

-0.3579

 

71.77419

-0.54265

 

 

46

-1.487037371

-0.01664

-0.03307

 

73.3871

-0.46521

 

 

47

-1.478247151

0.037539

0.074622

 

75

-0.42361

 

 

48

-1.413649192

0.492175

0.978378

 

76.6129

-0.42243

 

 

49

-1.524505922

0.245679

0.488377

 

78.22581

-0.40583

 

 

50

-1.487450643

0.292935

0.582315

 

79.83871

-0.35375

 

 

51

-1.505251423

0.190142

0.377976

 

81.45161

-0.34252

 

 

52

-1.527381021

0.148409

0.295016

 

83.06452

-0.31369

 

 

53

-1.482557579

-0.14417

-0.2866

 

84.67742

-0.30185

 

 

54

-1.52380675

-0.00829

-0.01648

 

86.29032

-0.20625

 

 

55

-1.390485216

-0.11828

-0.23513

 

87.90323

-0.15059

 

 

56

-1.337707601

0.005248

0.010433

 

89.51613

-0.13132

 

 

57

-1.499050031

0.023363

0.046443

 

91.12903

-0.11304

 

 

58

-1.500100106

-0.03278

-0.06516

 

92.74194

-0.09082

 

 

59

-1.463185951

-0.07514

-0.14936

 

94.35484

-0.02374

 

 

60

-1.358091228

0.177451

0.352749

 

95.96774

-0.00641

 

 

61

-1.349970557

0.346514

0.688822

 

97.58065

0

 

 

62

-1.479078582

0.457199

0.90885

 

99.19355

0.096848

 

 

figure.jpg

figure1.jpg

The CAPM for regression model infers that Boeng = 0.001GD + 0.60

This infers that there is no difference in CAMP of both stocks are fair value and no variation in their risk level

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Task B: Hypothesis Testing of Means and Variances Equality

Question 1: Calculate returns for these three series in Excel or any software of your choice using the transformation: rt = 100*ln(Pt / Pt-1) and perform the Jarque-Berra test of normally distributed returns for each of Boeing and GD. What do you infer about the distribution of the two stock returns series? Describe also the risk and average return relationship in each of the two stocks.

Answer:

JB_Boeng

JB_GD







27.9282161

22.9217












JB Test calculation







n[(K3)^2/6 + (k4)^2/24]

6.39E+08


The chi square critical value




33649.99







K3^2/6

5608.331


H0: Normal distribution of data



K4^2

2.47E+08


H1: Means there is no normal distribution of data


K4^2/24

10302090








10307699








6.39E+08










JB

Boeng

27.92

p<0.05> 0.01




JB

GD

22.92

p<0.05> 0.01












We usually do not take Null theory into account when the significance level is 5%

Question 2:

       Test a hypothesis that the average return on GD stock is different from 2.8%. Which test statistic would you choose to perform this hypothesis test and why? Also, specify the distribution of the test statistic under the null hypothesis.

Answer:

One-Sample Statistics

 

N

Mean

Std. Deviation

Std. Error Mean

rt_GD

62

1.1102

.37165

.04720

The mean GD stock rate is 1.11% with deviation of 0.37

One-Sample Test

 

Test Value = 2.8                                    

 

t

df

Sig. (2-tailed)

Mean Difference

95% Confidence Interval of the Difference

 

Lower

Upper

rt_GD

-35.802

61

.000

-1.68984

-1.7842

-1.5955

In regards to a Student T-test was led to assess the accompanying expressed theory

M1 = 28% normal returns of GD stocks are 2.8%.

H0: The mean returns of GD isn't approach to 2.8 percent

H1: The mean GD stock return is 2.8%

The outcomes propose that t(61) = 35.80, alpha = 0.000< 0.005 has a measurable noteworthy mean distinction 1.68. The mean supply of GD esteem is observed to be 1.11 which isn't rise to conjectured mean stock esteem 2.8% in this test. It is henceforth deduced that invalid speculation expressing that the normal return isn't rise to 2.8 percent for GD Stock is acknowledged

Question 3: Before investing in one of the two stocks, you first want to compare risk associated with each of the two stocks. Perform an appropriate hypothesis test using 5% significance level and interpret your results.

Answer:

F-Test Two-Sample for Variances




 

rt_Boeng

rt_GD

Mean

1.01746

1.110295

Variance

0.111919

0.138301

Observations

62

62

Df

61

61

F

0.809245


P(F<=f) one-tail

0.205428


F Critical one-tail

0.654094

 

Invalid theory H0: There is no mean distinction between hazard returns of Boeng and GD.

Interchange theory H1: The danger of putting resources into GD stocks is higher than Boeng stocks. A F test is led to assess the distinctions in mean hazard free return rates. The F(61) = 0.80, p<0.25 is lesser than F basic esteem (0.65). This construes recommending that there is a noteworthy variety in hazard related with GD and Boeng stocks. Henceforth, invalid theory is rejected. The hazard related with GD is higher than Boeng since mean returns of GD is higher than Boeng stocks.

Question 4: Besides, you want to determine whether both stocks have same population average return. Perform an appropriate hypothesis test using information in your sample of 60 observations on returns. Report your findings and also mention which stock will you prefer and why?

Answer:

H0: There is no mean varieties in normal returns of GD and Beong stocks

H1: There is a measurable critical mean contrast in populace normal returns of GD and Boeng stocks

Connection investigation was performed to evaluate whether there is any connection between populace normal returns of GD and Boeng stocks. The r esteem near 1 to - 1 demonstrates the positive to negative relationship held between factors  

 

rt_Boeng

rt_GD

rt_Boeng

1

1

rt_GD

0.95216012

1

As per the mentioned connection grid detailed that the loads of GD and Boeng have comparative populace mean returns, since, Pearson's r esteem is 0.95 at 95% C.I. This deduces recommending that populace normal of GD and Boeng stock returns have solid positive connection between them. Thus, invalid speculation is acknowledged.

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Task C: Regression Analysis and Inference

Question 5: Compute excess return on your preferred stock as yt = rt - rf,t   and excess market return as xt = rM,t - rf,t  and perform the following tasks.

Answer:

a. Estimate the CAPM using linear regression by regressing the excess return on your preferred stock (yt) on excess market return (xt) and properly report your regression results.

Relapse investigation is led to evaluate the peril of putting resources into GD stocks. The overabundance returns and market returns of GD stock were determined by subtracting the SP 500 returns and CBOE US treasury premium returns. CAMP Beta coefficient esteem is assessed utilizing relapse.

b. Interpret the estimated CAPM beta-coefficient in terms of the stock's riskiness in comparison with the market.

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

0.604712

0.294961

2.05014

0.044728

0.014702

1.194723

0.014702

1.194723

xt_GD

-0.00101

0.000173

-5.84383

2.24E-07

-0.00136

-0.00067

-0.00136

-0.00067

The Beta coefficient of CAMP GD stock is - 0.00101 is seen from the above determined Regression results.

c. Interpret the value of R2.

Regression Statistics

Multiple R

0.602263

R Square

0.362721

Adjusted R Square

0.3521

Standard Error

0.507227

Observations

62

The R squared estimation of the assessed CAPM model for GD stock is 0.36. This gathers this model gauges the danger of contributing GD stocks 36% correctly. Expanded dimension of standard blunder rate is the purpose behind less R squared esteem.

d. Interpret 95% confidence interval for the slope coefficient. 

Question 6: Using the confidence interval approach to hypothesis testing, perform the hypothesis test to determine whether your preferred stock is a neutral stock.

Answer:

H0: The abundance market returns of GD stock is seen to impartial

H1: The abundance market returns of GD stock is certainly not an unbiased stock

The t(- 5.85) has p esteem = 2.24 more noteworthy than p<0.005 at 95% C.I. Henceforth, it is obvious that invalid speculation is rejected. This gathers overabundance market returns of GD stock is certainly not an impartial stock and it is less hazardous in nature.

Question 7: One of the assumptions of ordinary least squares (OLS) method is; normally distributed error term in the model. Perform an appropriate hypothesis test to determine whether it is plausible to assume normally distributed errors.

Answer:

The blunder term in relapse model as a rule gauges the likelihood of expectation of relapse model. The evaluated standard blunder is 0.50.

Invalid Hypothesis H0: The mistake term isn't regularly disseminated

Substitute Hypothesis H1: The blunder term is dispersed ordinarily

The standard blunder of beta coefficient esteem is observed to be 0.00 at 5% hugeness dimension in the relapse table. This construes, invalid speculation expressing that blunder term isn't circulated regularly is acknowledged.

figure2.jpg

Moreover, the likelihood plot likewise displays the negative straight pattern suggesting that blunder term isn't regularly appropriated

Proposal

The mean stock returns of GD and Boeng were thought about by figuring the normal hazard free returns, abundance returns and market returns. The normal stock returns of GD are nearly higher than Boeng. Likewise, the hazard free return for GD stock is seen to be bigger than Boeng's without hazard return rate. Factual test were performed to looking at the populace mean of normal return and a positive solid connection was seen among GD and Boeng. Notwithstanding, results acquired from relapse testing has registered estimation of CAPM Beta Coefficient of GD stocks. This uncovered CAPM of GD stocks is exceedingly less secure at 5% Significance dimension. The overabundance returns of stock additionally delineate the solid negative association with the abundance market returns. Henceforth, it is more dangerous to put resources into GD stocks.

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