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SUMMARY OUTPUT
Regression Statistics
Multiple R 0.932474819
R Square 0.869509289
Adjusted R Square 0.85984331
Standard Error 0.791101451
Observations 30
ANOVA
df SS MS F Significance F
Regression 2###-##-####56.29797301 89.9556397 1.14901E-12
Residual 27 16.89772066 0.625841506
Total 29(###) ###-####
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -0.585965602 0.395227672 -1.482602673 0.14975908 -1.3969058 0.224974595 -1.3969058 0.224974595
Amount of Bill 0.098520271 0.020828316 4.730112106 6.29095E-05 0.055784096 0.141256446 0.055784096 0.141256446
Diners 0.598006485 0.232168395 2.575744578 0.015795727 0.121636287 1.074376683 0.121636287 1.074376683
Since all p values <0.05, the model is significant
RESIDUAL OUTPUT
Observation Predicted Amount of Tip Residuals Dependent variable Amount of tip
1 7.228604507 -0.228604507 Independent variable Amount of Bill, Diners
2 4.587287596 -0.087287596
3 1.061281772 -0.061281772
4 3.160725629 -0.760725629 Amount of tip = 0.09852 * Amount of Bill + 0.598006 * Diners - 0.58597
5 4.027704017 0.972295983
6 3.056305703 1.193694297 R Square 0.869509289
7 0.626807375 -0.126807375
8 6.653257684 -0.653257684 This means that the regression equation given above correctly predicts the amount of tip
9 5.470040788 -0.470040788 86.95% of the times
10 4.895656045 -0.145656045
11 5.044421654 0.205578346
12 4.655278144 1.344721856
13 5.146882737 -1.146882737
14 2.881924823 0.468075177
15 0.470160144 0.279839856
16 2.934140567 0.365859433
17 2.807049417 0.692950583
18 3.762696048 -0.512696048
19 6.734044307 -1.334044307
20 2.942010627 -0.692010627
21 6.187256801 -0.687256801
22 2.607053266 0.392946734
23 2.534148266 -1.284148266
24 3.871056785 -0.621056785
25 2.70655874 0.29344126
26 6.079869705 0.170130295
27 4.576450366 1.023549634
28 3.196204489 -0.696204489
29 8.001003434 1.248996566
30 7.394118563 0.855881437

 

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.056799

R Square

0.003226

Adjusted R Square

-0.01754

Standard Error

14.70467

Observations

50

ANOVA

 
 

df

SS

MS

F

Significance F

Regression

1

33.59251

33.59251

0.155357

0.695213

Residual

48

10378.91

216.2272

  

Total

49

10412.5

   
 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

33.32988

19.97358

1.668699

0.101688

-6.82969

73.48945

-6.82969

73.48945

Dependent variable

Rank

Age

-0.15697

0.398256

-0.39415

0.695213

-0.95772

0.643774

-0.95772

0.643774

Independent variable

Age

RESIDUAL OUTPUT

         

Observation

Predicted Rank

Residuals

Since Significane F > 0.05, the model is not significant

  

1

25.63814

-24.6381

        

2

25.16721

-23.1672

        

3

25.32419

-22.3242

        

4

25.32419

-21.3242

        

5

25.95209

-20.9521

        

6

25.16721

-19.1672

        

7

27.05091

-20.0509

        

8

26.57998

-18.58

        

9

24.53932

-15.5393

        

10

25.16721

-15.1672

        

11

25.63814

-14.6381

        

12

25.01024

-13.0102

        

13

24.69629

-11.6963

        

14

25.01024

-11.0102

        

15

25.79511

-10.7951

        

16

25.95209

-9.95209

        

17

25.32419

-8.32419

        

18

25.95209

-7.95209

        

19

25.48116

-6.48116

        

20

27.20788

-7.20788

        

21

23.28352

-2.28352

        

22

24.53932

-2.53932

        

23

25.79511

-2.79511

        

24

26.10906

-2.10906

        

25

25.63814

-0.63814

        

26

24.22537

1.774632

        

27

25.16721

1.832786

        

28

25.32419

2.675811

        

29

25.63814

3.361863

        

30

26.26603

3.733965

        

31

24.38234

6.617657

        

32

24.69629

7.303709

        

33

26.42301

6.576991

        

34

23.75445

10.24555

        

35

26.73696

8.263042

        

36

26.42301

9.576991

        

37

25.79511

11.20489

        

38

25.32419

12.67581

        

39

24.06839

14.93161

        

40

26.73696

13.26304

        

41

25.95209

15.04791

        

42

25.95209

16.04791

        

43

26.26603

16.73397

        

44

24.69629

19.30371

        

45

25.32419

19.67581

        

46

25.63814

20.36186

        

47

25.01024

21.98976

        

48

25.95209

22.04791

        

49

26.57998

22.42002

        

50

25.32419

24.67581

        

 

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.773219

R Square

0.597867

Adjusted R Square

0.569143

Standard Error

4.532206

Observations

46

ANOVA

 
 

df

SS

MS

F

Significance F

Regression

3

1282.635

427.5452

20.81434

2.03E-08

Residual

42

862.7175

20.54089

  

Total

45

2145.353

   
 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

43.076

7.200063

5.982726

4.21E-07

28.54569

57.60632

28.54569

57.60632

Literacy %

0.266381

0.082467

3.230172

0.002406

0.099957

0.432806

0.099957

0.432806

GDP/cap

0.329337

0.099237

3.318676

0.001876

0.129067

0.529606

0.129067

0.529606

Petroleum

1.805679

1.127651

1.601275

0.116812

-0.47001

4.081371

-0.47001

4.081371

Since P value of Petroleum > 0.05, it is statistically insignificant

   

RESIDUAL OUTPUT

       

Observation

Predicted Life Expectancy

Residuals

      

1

64.9078

5.042197

      

2

74.75601

0.503991

      

3

79.16042

0.709575

      

4

77.41479

0.425211

      

5

77.51359

0.44641

      

6

69.21194

-5.97194

      

7

78.88822

0.671781

      

8

67.77737

3.842626

      

9

73.93594

0.794059

      

10

79.9179

-3.1979

      

11

77.25594

0.324055

      

12

77.48357

1.416432

      

13

77.15423

0.455768

      

14

75.8525

2.737501

      

15

73.13633

-1.50633

      

16

77.88168

1.638316

      

17

59.45805

3.221947

      

18

69.96519

-1.69519

      

19

67.96828

1.981723

      

20

62.96082

3.989179

      

21

76.29504

0.694956

      

22

76.45971

2.680287

      

23

77.64824

3.151764

      

24

72.56498

3.705017

      

25

69.91672

5.733285

      

26

81.70199

-4.40199

      

27

71.74641

0.013586

      

28

79.28925

-0.85925

      

29

75.27701

2.712987

      

30

62.21061

-11.1406

      

31

80.64244

-1.85244

      

32

72.24712

1.172882

      

33

71.56125

4.37875

      

34

74.41702

-1.79702

      

35

73.52295

-6.18295

      

36

66.87414

1.215856

      

37

67.47889

-19.3889

      

38

74.48369

0.166306

      

39

74.84305

4.086948

      

40

76.75903

2.950972

      

41

78.86678

0.863219

      

42

67.95791

3.282093

      

43

75.29364

-1.00364

      

44

78.76231

-0.94231

      

45

82.64266

-5.38266

      

46

72.99659

0.313411

      

 

 

 

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