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Logistic Regression


Case Processing Summary

Unweighted Cases(a)

N

Percent

Selected Cases

Included in Analysis

92

100.0

Missing Cases

0

.0

Total

92

100.0

Unselected Cases

0

.0

Total

92

100.0

a If weight is in effect, see classification table for the total number of cases.



Dependent Variable Encoding

Original Value

Internal Value

Bajo

0

Alto

1




Categorical Variables Codings



Frequency

Parameter coding

(1)

FUMA

No

64

1.000

Si

28

.000



Block 0: Beginning Block


Classification Table(a,b)



Predicted

PULSOREP

Percentage Correct




Observed

Bajo

Alto



Step 0

PULSOREP

Bajo

70

0

100.0

Alto

22

0

.0

Overall Percentage







76.1

a Constant is included in the model.

b The cut value is .500




Variables in the Equation



B

S.E.

Wald

df

Sig.

Exp(B)

Step 0

Constant

-1.157

.244

22.425

1

.000

.314




Variables not in the Equation



Score

df

Sig.

Step 0

Variables

FUMA(1)

3.081

1

.079

PESO

2.721

1

.099

Overall Statistics

7.249

2

.027



Block 1: Method = Enter


Omnibus Tests of Model Coefficients



Chi-square

df

Sig.

Step 1

Step

7.574

2

.023

Block

7.574

2

.023

Model

7.574

2

.023




Model Summary

Step

-2 Log likelihood

Cox & Snell R Square

Nagelkerke R Square

1

93.640

.079

.118




Hosmer and Lemeshow Test

Step

Chi-square

df

Sig.

1

7.561

8

.477




Contingency Table for Hosmer and Lemeshow Test



PULSOREP = Bajo

PULSOREP = Alto

Total

Observed

Expected

Observed

Expected



Step 1

1

9

8.345

0

.655

9

2

10

9.591

1

1.409

11

3

8

9.322

3

1.678

11

4

7

7.379

2

1.621

9

5

6

7.119

3

1.881

9

6

9

6.782

0

2.218

9

7

7

7.213

3

2.787

10

8

6

5.419

2

2.581

8

9

4

5.532

5

3.468

9

10

4

3.299

3

3.701

7




Classification Table(a)



Predicted

PULSOREP

Percentage Correct




Observed

Bajo

Alto



Step 1

PULSOREP

Bajo

68

2

97.1

Alto

20

2

9.1

Overall Percentage







76.1

a The cut value is .500




Variables in the Equation



B

S.E.

Wald

df

Sig.

Exp(B)

95.0% C.I.for EXP(B)

Lower

Upper

Step 1(a)

FUMA(1)

-1.193

.553

4.654

1

.031

.303

.103

.897

PESO

-.025

.012

4.169

1

.041

.975

.952

.999

Constant

3.180

1.871

2.888

1

.089

24.050







a Variable(s) entered on step 1: FUMA, PESO.

Step number: 1

Observed Groups and Predicted Probabilities

16 ô ô


ó ó

ó ó


F ó ó

R 12 ô ô


E ó A ó

Q ó B ó


U ó B ó

E 8 ô B ô

N ó B B ó

C ó BA AA B ó

Y ó BAABA B A B A ó

4 ô BBBBB ABB A B A ô

ó B B BBBBBABBB B B B A ó

ó B B BBBBBBBBBABAB B B ó

ó B BBBBBBBBBBBBBBBBBAB BAA AB A A B B ó

Predicted òòòòòòòòòòòòòòôòòòòòòòòòòòòòòôòòòòòòòòòòòòòòôòòòòòòòòòòòòòòò

Prob: 0 .25 .5 .75 1

Group: BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

Predicted Probability is of Membership for Alto

The Cut Value is .50

Symbols: B - Bajo

A - Alto


Each Symbol Represents 1 Case.

Ejemplo con HATCO

Tomando la base de datos de HATCO donde:


X1 - Rapidez de entregas

X2 - Nivel de precios percibido

X3 - Flexibilidad en precios (para negociar)

X4 - Imagen de manufactura

X5 - Service global necesario para mantener satifacción del cliente

X6 - Imagen de la fuerza de ventas

X7 - Calidad del producto pericbida por los clientes

X8 - Tamaño de la mepresa: 1 = grande; 0 = pequeña.

X9 - Nivel de utilización, porcentaje de productos adquiridos de Hatco

X10 - Nivel de satisfacción del cliente, en las mismas unidades que las percepciones X1 a X7

X11 - Uso de especificaciones: 1 - Valor; 0-con especificaciones.

X12 - Estrutura del abastecimiento: 1-Centralizado; 0-Descentralizado

X13 - Tipo de industria: 1 - industria A; 0 - otras industrias.

X14 - Tipo de situación de compra para el cliente: 1-Nueva tarea; 2-Compra modificada; 3-Compra normal

n

X1

X2

X3

X4

X5

X6

X7

X8

X9

X10

X11

X12

X13

X14

1

4.1

0.6

6.9

4.7

2.4

2.3

5.2

0

32

4.2

1

0

1

1

2

1.8

3

6.3

6.6

2.5

4

8.4

1

43

4.3

0

1

0

1

3

3.4

5.2

5.7

6

4.3

2.7

8.2

1

48

5.2

0

1

1

2

4

2.7

1

7.1

5.9

1.8

2.3

7.8

1

32

3.9

0

1

1

1

5

6

0.9

9.6

7.8

3.4

4.6

4.5

0

58

6.8

1

0

1

3

6

1.9

3.3

7.9

4.8

2.6

1.9

9.7

1

45

4.4

0

1

1

2

7

4.6

2.4

9.5

6.6

3.5

4.5

7.6

0

46

5.8

1

0

1

1

8

1.3

4.2

6.2

5.1

2.8

2.2

6.9

1

44

4.3

0

1

0

2

9

5.5

1.6

9.4

4.7

3.5

3

7.6

0

63

5.4

1

0

1

3

10

4

3.5

6.5

6

3.7

3.2

8.7

1

54

5.4

0

1

0

2

11

2.4

1.6

8.8

4.8

2

2.8

5.8

0

32

4.3

1

0

0

1

12

3.9

2.2

9.1

4.6

3

2.5

8.3

0

47

5

1

0

1

2

13

2.8

1.4

8.1

3.8

2.1

1.4

6.6

1

39

4.4

0

1

0

1

14

3.7

1.5

8.6

5.7

2.7

3.7

6.7

0

38

5

1

0

1

1

15

4.7

1.3

9.9

6.7

3

2.6

6.8

0

54

5.9

1

0

0

3

16

3.4

2

9.7

4.7

2.7

1.7

4.8

0

49

4.7

1

0

0

3

17

3.2

4.1

5.7

5.1

3.6

2.9

6.2

0

38

4.4

1

1

1

2

18

4.9

1.8

7.7

4.3

3.4

1.5

5.9

0

40

5.6

1

0

0

2

19

5.3

1.4

9.7

6.1

3.3

3.9

6.8

0

54

5.9

1

0

1

3

20

4.7

1.3

9.9

6.7

3

2.6

6.8

0

55

6

1

0

0

3

21

3.3

0.9

8.6

4

2.1

1.8

6.3

0

41

4.5

1

0

0

2

22

3.4

0.4

8.3

2.5

1.2

1.7

5.2

0

35

3.3

1

0

0

1

23

3

4

9.1

7.1

3.5

3.4

8.4

0

55

5.2

1

1

0

3

24

2.4

1.5

6.7

4.8

1.9

2.5

7.2

1

36

3.7

0

1

0

1

25

5.1

1.4

8.7

4.8

3.3

2.6

3.8

0

49

4.9

1

0

0

2

26

4.6

2.1

7.9

5.8

3.4

2.8

4.7

0

49

5.9

1

0

1

3

27

2.4

1.5

6.6

4.8

1.9

2.5

7.2

1

36

3.7

0

1

0

1

28

5.2

1.3

9.7

6.1

3.2

3.9

6.7

0

54

5.8

1

0

1

3

29

3.5

2.8

9.9

3.5

3.1

1.7

5.4

0

49

5.4

1

0

1

3

30

4.1

3.7

5.9

5.5

3.9

3

8.4

1

46

5.1

0

1

0

2

31

3

3.2

6

5.3

3.1

3

8

1

43

3.3

0

1

0

1

32

2.8

3.8

8.9

6.9

3.3

3.2

8.2

0

53

5

1

1

0

3

33

5.2

2

9.3

5.9

3.7

2.4

4.6

0

60

6.1

1

0

0

3

34

3.4

3.7

6.4

5.7

3.5

3.4

8.4

1

47.3

3.8

0

1

0

1

35

2.4

1

7.7

3.4

1.7

1.1

6.2

1

35

4.1

0

1

0

1

36

1.8

3.3

7.5

4.5

2.5

2.4

7.6

1

39

3.6

0

1

1

1

37

3.6

4

5.8

5.8

3.7

2.5

9.3

1

44

4.8

0

1

1

2

38

4

0.9

9.1

5.4

2.4

2.6

7.3

0

46

5.1

1

0

1

3

39

0

2.1

6.9

5.4

1.1

2.6

8.9

1

29

3.9

0

1

1

1

40

2.4

2

6.4

4.5

2.1

2.2

8.8

1

28

3.3

0

1

1

1

41

1.9

3.4

7.6

4.6

2.6

2.5

7.7

1

40

3.7

0

1

1

1

42

5.9

0.9

9.6

7.8

3.4

4.6

4.5

0

58

6.7

1

0

1

3

43

4.9

2.3

9.3

4.5

3.6

1.3

6.2

0

53

5.9

1

0

0

3

44

5

1.3

8.6

4.7

3.1

2.5

3.7

0

48

4.8

1

0

0

2

45

2

2.6

6.5

3.7

2.4

1.7

8.5

1

38

3.2

0

1

1

1

46

5

2.5

9.4

4.6

3.7

1.4

6.3

0

54

6

1

0

0

3

47

3.1

1.9

10

4.5

2.6

3.2

3.8

0

55

4.9

1

0

1

3

48

3.4

3.9

5.6

5.6

3.6

2.3

9.1

1

43

4.7

0

1

1

2

49

5.8

0.2

8.8

4.5

3

2.4

6.7

0

57

4.9

1

0

1

3

50

5.4

2.1

8

3

3.8

1.4

5.2

0

53

3.8

1

0

1

3

51

3.7

0.7

8.2

6

2.1

2.5

5.2

0

41

5

1

0

0

2

52

2.6

4.8

8.2

5

3.6

2.5

9

1

53

5.2

0

1

1

2

53

4.5

4.1

6.3

5.9

4.3

3.4

8.8

1

50

5.5

0

1

0

2

54

2.8

2.4

6.7

4.9

2.5

2.6

9.2

1

32

3.7

0

1

1

1

55

3.8

0.8

6.7

2.9

1.6

2.1

5.6

0

39

3.7

1

0

0

1

56

2.9

2.6

7.7

7

2.8

3.6

7.7

0

47

4.2

1

1

1

2

57

4.9

4.4

7.4

6.9

4.6

4

9.6

1

62

6.2

0

1

0

2

58

5.4

2.5

9.6

5.5

4

3

7.7

0

65

6

1

0

0

3

59

4.3

1.8

7.6

5.4

3.1

2.5

4.4

0

46

5.6

1

0

1

3

60

2.3

4.5

8

4.7

3.3

2.2

8.7

1

50

5

0

1

1

2

61

3.1

1.9

9.9

4.5

2.6

3.1

3.8

0

54

4.8

1

0

1

3

62

5.1

1.9

9.2

5.8

3.6

2.3

4.5

0

60

6.1

1

0

0

3

63

4.1

1.1

9.3

5.5

2.5

2.7

7.4

0

47

5.3

1

0

1

3

64

3

3.8

5.5

4.9

3.4

2.6

6

0

36

4.2

1

1

1

2

65

1.1

2

7.2

4.7

1.6

3.2

10

1

40

3.4

0

1

1

1

66

3.7

1.4

9

4.5

2.6

2.3

6.8

0

45

4.9

1

0

0

2

67

4.2

2.5

9.2

6.2

3.3

3.9

7.3

0

59

6

1

0

0

3

68

1.6

4.5

6.4

5.3

3

2.5

7.1

1

46

4.5

0

1

0

2

69

5.3

1.7

8.5

3.7

3.5

1.9

4.8

0

58

4.3

1

0

0

3

70

2.3

3.7

8.3

5.2

3

2.3

9.1

1

49

4.8

0

1

1

2

71

3.6

5.4

5.9

6.2

4.5

2.9

8.4

1

50

5.4

0

1

1

2

72

5.6

2.2

8.2

3.1

4

1.6

5.3

0

55

3.9

1

0

1

3

73

3.6

2.2

9.9

4.8

2.9

1.9

4.9

0

51

4.9

1

0

0

3

74

5.2

1.3

9.1

4.5

3.3

2.7

7.3

0

60

5.1

1

0

1

3

75

3

2

6.6

6.6

2.4

2.7

8.2

1

41

4.1

0

1

0

1

76

4.2

2.4

9.4

4.9

3.2

2.7

8.5

0

49

5.2

1

0

1

2

77

3.8

0.8

8.3

6.1

2.2

2.6

5.3

0

42

5.1

1

0

0

2

78

3.3

2.6

9.7

3.3

2.9

1.5

5.2

0

47

5.1

1

0

1

3

79

1

1.9

9.1

4.5

1.5

3.1

9.9

1

39

3.3

0

1

1

1

80

4.5

1.6

8.7

4.6

3.1

2.1

6.8

0

56

5.1

1

0

0

3

81

5.5

1.8

8.7

3.8

3.6

2.1

4.9

0

59

4.5

1

0

0

3

82

3.4

4.6

5.5

8.2

4

4.4

6.3

0

47.3

5.6

1

1

1

2

83

1.6

2.8

6.1

6.4

2.3

3.8

8.2

1

41

4.1

0

1

0

1

84

2.3

3.7

7.6

5

3

2.5

7.4

0

37

4.4

1

1

0

1

85

2.6

3

8.5

6

2.8

2.8

6.8

1

53

5.6

0

1

0

2

86

2.5

3.1

7

4.2

2.8

2.2

9

1

43

3.7

0

1

1

1

87

2.4

2.9

8.4

5.9

2.7

2.7

6.7

1

51

5.5

0

1

0

2

88

2.1

3.5

7.4

4.8

2.8

2.3

7.2

0

36

4.3

1

1

0

1

89

2.9

1.2

7.3

6.1

2

2.5

8

1

34

4

0

1

1

1

90

4.3

2.5

9.3

6.3

3.4

4

7.4

0

60

6.1

1

0

0

3

91

3

2.8

7.8

7.1

3

3.8

7.9

0

49

4.4

1

1

1

2

92

4.8

1.7

7.6

4.2

3.3

1.4

5.8

0

39

5.5

1

0

0

2

93

3.1

4.2

5.1

7.8

3.6

4

5.9

0

43

5.2

1

1

1

2

94

1.9

2.7

5

4.9

2.2

2.5

8.2

1

36

3.6

0

1

0

1

95

4

0.5

6.7

4.5

2.2

2.1

5

0

31

4

1

0

1

1

96

0.6

1.6

6.4

5

0.7

2.1

8.4

1

25

3.4

0

1

1

1

97

6.1

0.5

9.2

4.8

3.3

2.8

7.1

0

60

5.2

1

0

1

3

98

2

2.8

5.2

5

2.4

2.7

8.4

1

38

3.7

0

1

0

1

99

3.1

2.2

6.7

6.8

2.6

2.9

8.4

1

42

4.3

0

1

0

1

100

2.5

1.8

9

5

2.2

3

6

0

33

4.4

1

0

0

1

Paso 1. Obtener el comportamiento del modelo por cada variable X1 a X7:


La variable dependiente es X11:
Corrida en Minitab:
1    Abrir la hoja de trabajo HATCO.MTW o tomar datos de esta tabla.

2    Seleccionar Stat > Regression > Binary Logistic Regression.

3    En Response, seleccionar X11 En Model, seleccionar X1-X7

4    Click Graphs. Seleccionar Delta chi-square vs probability y Delta chi-square vs leverage. Click OK.

5    Click Results. Seleccionar In addition, list of factor level values, tests for terms with more than 1 degree of freedom, and 2 additional goodness-of-fit tests. Click OK en cada uno de las ventanas de diálogo.

Model: Especificar los términos a ser incluidos en el modelo.

Los resultados de la corrida son los siguientes:


Binary Logistic Regression: X11 versus X1, X2, X3, X4, X5, X6, X7

Link Function: Logit

Response Information
Variable Value Count

X11 1 60 (Event)

0 40


Total 100

Logistic Regression Table

95% CI

Predictor Coef SE Coef Z P Odds Ratio Lower Upper



Constant -1.37522 5.27926 -0.26 0.794

X1 0.0759455 4.00067 0.02 0.985 1.08 0.00 2744.24

X2 -0.349077 4.00277 -0.09 0.931 0.71 0.00 1801.48

X3 2.21451 0.869462 2.55 0.011 9.16 1.67 50.33

X4 -2.04458 1.75315 -1.17 0.244 0.13 0.00 4.02

X5 2.63834 8.25052 0.32 0.749 13.99 0.00 1.47505E+08

X6 5.10396 2.97675 1.71 0.086 164.67 0.48 56297.08

X7 -3.39040 1.09301 -3.10 0.002 0.03 0.00 0.29

Log-Likelihood = -12.479

Test that all slopes are zero: G = 109.645, DF = 7, P-Value = 0.000

Goodness-of-Fit Tests
Method Chi-Square DF P

Pearson 41.5472 91 1.000

Deviance 24.9571 91 1.000

Hosmer-Lemeshow 2.0928 8 0.978

Brown:

General Alternative 2.5040 2 0.286



Symmetric Alternative 0.0018 1 0.966

Table of Observed and Expected Frequencies:

(See Hosmer-Lemeshow Test for the Pearson Chi-Square Statistic)
Group

Value 1 2 3 4 5 6 7 8 9 10 Total

1

Obs 0 0 0 2 9 9 10 10 10 10 60



Exp 0.0 0.0 0.3 2.1 8.0 9.6 9.9 10.0 10.0 10.0

0

Obs 10 10 10 8 1 1 0 0 0 0 40



Exp 10.0 10.0 9.7 7.9 2.0 0.4 0.1 0.0 0.0 0.0

Total 10 10 10 10 10 10 10 10 10 10 100

Measures of Association:

(Between the Response Variable and Predicted Probabilities)


Pairs Number Percent Summary Measures

Concordant 2375 99.0 Somers' D 0.98

Discordant 25 1.0 Goodman-Kruskal Gamma 0.98

Ties 0 0.0 Kendall's Tau-a 0.47



Total 2400 100.0







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