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Statistical Methods and Data Analytics

Applied Logistic Regression, Second Edition, by Hosmer and Lemeshow Chapter 3: Interpretation of the fitted logistic regression model | SPSS Textbook Examples

page 51 Table 3.2 Cross-classification of age dichotomized at 55 years and chd for 100 subjects

get file='chdage.sav'.

recode age (55 thru highest=1) (else=0) into aged.
execute.

CROSSTABS
  /TABLES=chd  BY aged
  /FORMAT= AVALUE TABLES
  /CELLS= COUNT.
Case Processing Summary

Cases
Valid Missing Total
N Percent N Percent N Percent
CHD * AGED 100 100.0% 0 .0% 100 100.0%


CHD * AGED Crosstabulation
Count

AGED Total
.00 1.00
CHD .00 51 6 57
1.00 22 21 43
Total 73 27 100

page 52 Table 3.3 Results of fitting the logistic regression model to the data in Table 3.2. 

LOGISTIC REGRESSION VAR=chd
  /METHOD=ENTER aged.
Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 100 100.0
Missing Cases 0 .0
Total 100 100.0
Unselected Cases 0 .0
Total 100 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
CHD Percentage Correct

Observed .00 1.00
Step 0 CHD .00 57 0 100.0
1.00 43 0 .0
Overall Percentage

57.0
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 -.282 .202 1.947 1 .163 .754

Variables not in the Equation

Score df Sig.
Step 0 Variables AGED 18.252 1 .000
Overall Statistics 18.252 1 .000

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 18.704 1 .000
Block 18.704 1 .000
Model 18.704 1 .000

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 117.959 .171 .229


Classification Table(a)

Predicted
CHD Percentage Correct

Observed .00 1.00
Step 1 CHD .00 51 6 89.5
1.00 22 21 48.8
Overall Percentage

72.0
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) AGED 2.094 .529 15.690 1 .000 8.114
Constant -.841 .255 10.865 1 .001 .431
a Variable(s) entered on step 1: AGED.

page 56 Table 3.5 Cross-classification of hypothetical data on race and chd status for 100 subjects. 

data list list / race chd cnt.
begin data.
 1 1 5
  2 1 20
  3 1 15
  4 1 10
  1 0 20
  2 0 10
  3 0 10
  4 0 10
end data.
execute .

weight by cnt.

CROSSTABS
  /TABLES=chd BY race
  /FORMAT= AVALUE TABLES
  /CELLS= COUNT .
Case Processing Summary

Cases
Valid Missing Total
N Percent N Percent N Percent
CHD * RACE 100 100.0% 0 .0% 100 100.0%


CHD * RACE Crosstabulation
Count

RACE Total
1.00 2.00 3.00 4.00
CHD .00 20 10 10 10 50
1.00 5 20 15 10 50
Total 25 30 25 20 100
  
LOGISTIC REGRESSION VAR=chd
  /METHOD=ENTER race
  /CONTRAST (race)=Indicator(1)
  /PRINT=SUMMARY CI(95).
Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 8 100.0
Missing Cases 0 .0
Total 8 100.0
Unselected Cases 0 .0
Total 8 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1

Categorical Variables Codings

Frequency Parameter coding
(1) (2) (3)
RACE 1.00 2 .000 .000 .000
2.00 2 1.000 .000 .000
3.00 2 .000 1.000 .000
4.00 2 .000 .000 1.000


Classification Table(a,b)

Predicted
CHD Percentage Correct

Observed .00 1.00
Step 0 CHD .00 0 50 .0
1.00 0 50 100.0
Overall Percentage

50.0
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 .000 .200 .000 1 1.000 1.000

Variables not in the Equation

Score df Sig.
Step 0 Variables RACE 13.333 3 .004
RACE(1) 4.762 1 .029
RACE(2) 1.333 1 .248
RACE(3) .000 1 1.000
Overall Statistics 13.333 3 .004

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 14.042 3 .003
Block 14.042 3 .003
Model 14.042 3 .003

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 124.587 .131 .175


Classification Table(a)

Predicted
CHD Percentage Correct

Observed .00 1.00
Step 1 CHD .00 20 30 40.0
1.00 5 45 90.0
Overall Percentage

65.0
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) RACE

11.771 3 .008


RACE(1) 2.079 .632 10.810 1 .001 8.000 2.316 27.633
RACE(2) 1.792 .645 7.705 1 .006 6.000 1.693 21.261
RACE(3) 1.386 .671 4.271 1 .039 4.000 1.074 14.895
Constant -1.386 .500 7.687 1 .006 .250

a Variable(s) entered on step 1: RACE.

NOTE: The above code also gives the coding scheme shown in Table 3.6.

page 58 Table 3.7 Results of fitting the logistic regression model to the data in Table 3.5 using the design variables in Table 3.6.

NOTE: The above code also gives the output shown in Table 3.7.

page 59 Table 3.8 Specification of the design variables for race using deviation from means coding. 

LOGISTIC REGRESSION VAR=chd
  /METHOD=ENTER race
  /CONTRAST (race)=Deviation(1)
  /PRINT=SUMMARY CI(95).
Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 8 100.0
Missing Cases 0 .0
Total 8 100.0
Unselected Cases 0 .0
Total 8 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1

Categorical Variables Codings

Frequency Parameter coding
(1) (2) (3)
RACE 1.00 2 -1.000 -1.000 -1.000
2.00 2 1.000 .000 .000
3.00 2 .000 1.000 .000
4.00 2 .000 .000 1.000


Classification Table(a,b)

Predicted
CHD Percentage Correct

Observed .00 1.00
Step 0 CHD .00 0 50 .0
1.00 0 50 100.0
Overall Percentage

50.0
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 .000 .200 .000 1 1.000 1.000

Variables not in the Equation

Score df Sig.
Step 0 Variables RACE 13.333 3 .004
RACE(1) 11.416 1 .001
RACE(2) 8.000 1 .005
RACE(3) 5.028 1 .025
Overall Statistics 13.333 3 .004

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 14.042 3 .003
Block 14.042 3 .003
Model 14.042 3 .003

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 124.587 .131 .175


Classification Table(a)

Predicted
CHD Percentage Correct

Observed .00 1.00
Step 1 CHD .00 20 30 40.0
1.00 5 45 90.0
Overall Percentage

65.0
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) RACE

11.771 3 .008


RACE(1) .765 .351 4.762 1 .029 2.149 1.081 4.273
RACE(2) .477 .362 1.736 1 .188 1.612 .792 3.279
RACE(3) .072 .385 .035 1 .852 1.075 .506 2.284
Constant -.072 .219 .108 1 .743 .931

a Variable(s) entered on step 1: RACE.

page 60 Table 3.9 Results of fitting the logistic regression model to the data in Table 3.5 using the design variables in Table 3.8.

NOTE: The above code also gives the output shown in Table 3.9.

NOTE: To get the values listed in the column labeled z, you need to take the square root of the Wald statistics given in the SPSS output.

page 67 Table 3.10 Descriptive statistics for two groups of 50 men on age and whether they had seen a physician (PHY) (1 = yes, 0 = no) within the last six months.

NOTE: These data are hypothetical and are not available.

page 69 Table 3.11 Results of fitting the logistic regression model to the data summarized in Table 3.10.

NOTE: These data are hypothetical and are not available.

page 72 Table 3.12 Estimated logistic regression coefficients, deviance, and the likelihood ratio test statistic (G) for an example showing evidence of confounding but no interaction (n = 400).

NOTE: These data are hypothetical and are not available.

page 73 Table 3.13 Estimated logistic regression coefficients, deviance, and the likelihood ratio test statistic (G) for an example showing evidence of confounding and interaction (n = 400).

NOTE: These data are hypothetical and are not available.

page 77 Table 3.14 Estimated logistic regression coefficients, deviance, and the likelihood ratio test statistic (G), and the p-value for the change for models containing lwd and age from the low birth weight data (n = 189).

NOTE: We have run the logistic regression models from the largest to the smallest so that the difference between the larger and the smaller model can be determined. This is the reverse of the presentation in the table in the book.

NOTE: To get the ln[l(beta)], divide the -2 log likelihood given in the output by -2. To obtain the values of G, subtract the value of ln[l(beta)]. from that of the model with one more term in it (for example,  -117.34-(-113.12)=8.44). 

Get file='lowbwt.sav'.

compute lwd=(lwt<110).
compute lwdage=lwd*age.
execute.

LOGISTIC REGRESSION VAR=low
  /METHOD=ENTER lwd age lwdage.
Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 189 100.0
Missing Cases 0 .0
Total 189 100.0
Unselected Cases 0 .0
Total 189 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 0 < 2500g .00 130 0 100.0
1.00 59 0 .0
Overall Percentage

68.8
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 -.790 .157 25.327 1 .000 .454

Variables not in the Equation

Score df Sig.
Step 0 Variables LWD 8.873 1 .003
AGE 2.674 1 .102
LWDAGE 9.639 1 .002
Overall Statistics 13.357 3 .004

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 13.532 3 .004
Block 13.532 3 .004
Model 13.532 3 .004

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 221.140 .069 .097


Classification Table(a)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 1 < 2500g .00 124 6 95.4
1.00 47 12 20.3
Overall Percentage

72.0
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) LWD -1.944 1.725 1.270 1 .260 .143
AGE -.080 .040 4.029 1 .045 .924
LWDAGE .132 .076 3.049 1 .081 1.141
Constant .774 .910 .724 1 .395 2.169
a Variable(s) entered on step 1: LWD, AGE, LWDAGE. 
LOGISTIC REGRESSION VAR=low
  /METHOD=ENTER lwd age.
Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 189 100.0
Missing Cases 0 .0
Total 189 100.0
Unselected Cases 0 .0
Total 189 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 0 < 2500g .00 130 0 100.0
1.00 59 0 .0
Overall Percentage

68.8
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 -.790 .157 25.327 1 .000 .454

Variables not in the Equation

Score df Sig.
Step 0 Variables LWD 8.873 1 .003
AGE 2.674 1 .102
Overall Statistics 10.670 2 .005

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 10.385 2 .006
Block 10.385 2 .006
Model 10.385 2 .006

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 224.287 .053 .075


Classification Table(a)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 1 < 2500g .00 115 15 88.5
1.00 50 9 15.3
Overall Percentage

65.6
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) LWD 1.010 .364 7.690 1 .006 2.746
AGE -.044 .032 1.884 1 .170 .957
Constant -.027 .762 .001 1 .972 .973
a Variable(s) entered on step 1: LWD, AGE. 
LOGISTIC REGRESSION VAR=low
  /METHOD=ENTER lwd.
Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 189 100.0
Missing Cases 0 .0
Total 189 100.0
Unselected Cases 0 .0
Total 189 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 0 < 2500g .00 130 0 100.0
1.00 59 0 .0
Overall Percentage

68.8
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 -.790 .157 25.327 1 .000 .454

Variables not in the Equation

Score df Sig.
Step 0 Variables LWD 8.873 1 .003
Overall Statistics 8.873 1 .003

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 8.431 1 .004
Block 8.431 1 .004
Model 8.431 1 .004

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 226.241 .044 .061


Classification Table(a)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 1 < 2500g .00 109 21 83.8
1.00 38 21 35.6
Overall Percentage

68.8
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) LWD 1.054 .362 8.494 1 .004 2.868
Constant -1.054 .188 31.288 1 .000 .349
a Variable(s) entered on step 1: LWD.

NOTE: To get the model with only the intercept, you need to create a variable equal to one and use that as the dependent variable. 

compute x = 1.

 LOGISTIC REGRESSION VAR=low
  /METHOD=ENTER x
  /ORIGIN.
Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 189 100.0
Missing Cases 0 .0
Total 189 100.0
Unselected Cases 0 .0
Total 189 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b,c)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 0 < 2500g .00 0 130 .0
1.00 0 59 100.0
Overall Percentage

31.2
a No terms in the model.
b Initial Log-likelihood Function: -2 Log Likelihood = 262.010
c The cut value is .500

Variables not in the Equation

Score df Sig.
Step 0 Variables X 26.672 1 .000
Overall Statistics 26.672 1 .000

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 27.338 1 .000
Block 27.338 1 .000
Model 27.338 1 .000

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 234.672 .135 .180


Classification Table(a)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 1 < 2500g .00 130 0 100.0
1.00 59 0 .0
Overall Percentage

68.8
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) X -.790 .157 25.327 1 .000 .454
a Variable(s) entered on step 1: X.
 

page 78 Figure 3.3 Plot of the estimated logit for women with LWD = 1 and for women with LWD = 0 from Model 3 in Table 3.17. 

LOGISTIC REGRESSION VAR=low
  /METHOD=ENTER lwd age lwdage
  /SAVE PRED.
Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 189 100.0
Missing Cases 0 .0
Total 189 100.0
Unselected Cases 0 .0
Total 189 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 0 < 2500g .00 130 0 100.0
1.00 59 0 .0
Overall Percentage

68.8
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 -.790 .157 25.327 1 .000 .454

Variables not in the Equation

Score df Sig.
Step 0 Variables LWD 8.873 1 .003
AGE 2.674 1 .102
LWDAGE 9.639 1 .002
Overall Statistics 13.357 3 .004

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 13.532 3 .004
Block 13.532 3 .004
Model 13.532 3 .004

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 221.140 .069 .097


Classification Table(a)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 1 < 2500g .00 124 6 95.4
1.00 47 12 20.3
Overall Percentage

72.0
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) LWD -1.944 1.725 1.270 1 .260 .143
AGE -.080 .040 4.029 1 .045 .924
LWDAGE .132 .076 3.049 1 .081 1.141
Constant .774 .910 .724 1 .395 2.169
a Variable(s) entered on step 1: LWD, AGE, LWDAGE. 
GRAPH
  /SCATTERPLOT(BIVAR)=age WITH pre_1.

Scatter of pre_1 age

page 78 Table 3.15 Estimated covariance matrix for the estimated parameters in Model 3 of Table 3.14.

NOTE: There are likely typos in this table. 

LOGISTIC REGRESSION VAR=low
  /METHOD=ENTER lwd age lwdage
  /PRINT=corr.
Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 189 100.0
Missing Cases 0 .0
Total 189 100.0
Unselected Cases 0 .0
Total 189 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 0 < 2500g .00 130 0 100.0
1.00 59 0 .0
Overall Percentage

68.8
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 -.790 .157 25.327 1 .000 .454

Variables not in the Equation

Score df Sig.
Step 0 Variables LWD 8.873 1 .003
AGE 2.674 1 .102
LWDAGE 9.639 1 .002
Overall Statistics 13.357 3 .004

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 13.532 3 .004
Block 13.532 3 .004
Model 13.532 3 .004

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 221.140 .069 .097


Classification Table(a)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 1 < 2500g .00 124 6 95.4
1.00 47 12 20.3
Overall Percentage

72.0
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) LWD -1.944 1.725 1.270 1 .260 .143
AGE -.080 .040 4.029 1 .045 .924
LWDAGE .132 .076 3.049 1 .081 1.141
Constant .774 .910 .724 1 .395 2.169
a Variable(s) entered on step 1: LWD, AGE, LWDAGE.

Correlation Matrix

Constant LWD AGE LWDAGE
Step 1 Constant 1.000 -.528 -.978 .512
LWD -.528 1.000 .516 -.977
AGE -.978 .516 1.000 -.524
LWDAGE .512 -.977 -.524 1.000

constant/constant: (.910)**2 = .8281 
constant/lwd: (.910)*(1.725)*(-.528) = -.828828 
constant/age: (.910)*(.040)*(-.978) = -.0355992 
constant/lwd*age: (.910)*(.076)*(.512) = .03603236 
lwd/lwd: (1.725)**2 = 2.975625 
lwd/age: (1.725)*(.040)*(.516) = .035604 
lwd/lwd*age: (1.725)*(.076)*(-.977) = -.1280847 
age/age: (.040)**2 = .0016 
age/lwd*age: (.040)*(.076)*(-.524) = -.001593 
lwd*age/lwd*age: (.076)**2 = .005776

page 79 Table 3.16 Estimated odds ratios and 95% confidence intervals for lwd, controlling for age.

NOTE: We were unable to reproduce this table.

page 80 Table 3.17 Cross-classification of low birth weight by smoking status. 

CROSSTABS
  /TABLES=low BY smoke
  /FORMAT= AVALUE TABLES
  /CELLS= COUNT.
Case Processing Summary

Cases
Valid Missing Total
N Percent N Percent N Percent
< 2500g * SMOKE 189 100.0% 0 .0% 189 100.0%


< 2500g * SMOKE Crosstabulation
Count

SMOKE Total
.00 1.00
< 2500g .00 86 44 130
1.00 29 30 59
Total 115 74 189

page 81 Table 3.18 Cross-classification of low birth weight by smoking status stratified by race. 

CROSSTABS
  /TABLES=low BY smoke BY race
  /FORMAT= AVALUE TABLES
  /CELLS= COUNT.
Case Processing Summary

Cases
Valid Missing Total
N Percent N Percent N Percent
< 2500g * SMOKE * RACE 189 100.0% 0 .0% 189 100.0%


< 2500g * SMOKE * RACE Crosstabulation
Count

SMOKE Total
RACE .00 1.00
white < 2500g .00 40 33 73
1.00 4 19 23
Total 44 52 96
black < 2500g .00 11 4 15
1.00 5 6 11
Total 16 10 26
other < 2500g .00 35 7 42
1.00 20 5 25
Total 55 12 67
 

page 82 Table 3.19 Tabulation of the estimated odds ratios, ln(estimated odds ratios), estimated variance of the ln(estimated odds ratios), and the inverse of the estimated variance, w, for smoking status within each stratum of race.

NOTE: The estimated variance of the ln(estimated odds ratios), and the inverse of the estimated variance, w, were not calculated  because they were needed only to do a hand-computation. 

compute race1=0.

recode race1 (0=1) (1,2=2) (3 thru 15=3) (16 thru highest=4).

recode race (2=1) (else=0) into race2.
recode race (3=1) (else=0) into race3.
compute race1sm=race1*smoke.
compute race2sm=race2*smoke.
compute race3sm=race3*smoke.
execute.

NOTE: Values for White: 

LOGISTIC REGRESSION VAR=low
  /METHOD=ENTER race2 race3 race2sm race3sm smoke.

Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 189 100.0
Missing Cases 0 .0
Total 189 100.0
Unselected Cases 0 .0
Total 189 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 0 < 2500g .00 130 0 100.0
1.00 59 0 .0
Overall Percentage

68.8
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 -.790 .157 25.327 1 .000 .454

Variables not in the Equation

Score df Sig.
Step 0 Variables RACE2 1.727 1 .189
RACE3 1.797 1 .180
RACE2SM 4.074 1 .044
RACE3SM .652 1 .420
SMOKE 4.924 1 .026
Overall Statistics 15.865 5 .007

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 17.854 5 .003
Block 17.854 5 .003
Model 17.854 5 .003

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 216.818 .090 .127


Classification Table(a)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 1 < 2500g .00 126 4 96.9
1.00 53 6 10.2
Overall Percentage

69.8
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) RACE2 1.514 .752 4.051 1 .044 4.545
RACE3 1.743 .595 8.592 1 .003 5.714
RACE2SM -.557 1.032 .291 1 .590 .573
RACE3SM -1.527 .883 2.993 1 .084 .217
SMOKE 1.750 .598 8.561 1 .003 5.757
Constant -2.303 .524 19.280 1 .000 .100
a Variable(s) entered on step 1: RACE2, RACE3, RACE2SM, RACE3SM, SMOKE.

NOTE: Values for Black: 

LOGISTIC REGRESSION VAR=low
  /METHOD=ENTER race1 race3 race1sm race3sm smoke.

Case Processing Summary
Unweighted Cases(b) N Percent
Selected Cases(a) Included in Analysis 189 100.0
Missing Cases 0 .0
Total 189 100.0
Unselected Cases 0 .0
Total 189 100.0
a The variable RACE1 is constant for all selected cases. Since a constant was requested in the model, it will be removed from the analysis.
b If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 0 < 2500g .00 130 0 100.0
1.00 59 0 .0
Overall Percentage

68.8
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 -.790 .157 25.327 1 .000 .454

Variables not in the Equation(a)

Score df Sig.
Step 0 Variables RACE3 1.797 1 .180
RACE1SM 4.924 1 .026
RACE3SM .652 1 .420
SMOKE 4.924 1 .026
a Residual Chi-Squares are not computed because of redundancies.

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 11.930 3 .008
Block 11.930 3 .008
Model 11.930 3 .008

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 222.742 .061 .086


Classification Table(a)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 1 < 2500g .00 130 0 100.0
1.00 59 0 .0
Overall Percentage

68.8
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) RACE3 1.175 .457 6.593 1 .010 3.237
RACE1SM 1.342 .445 9.111 1 .003 3.827
RACE3SM -1.119 .787 2.023 1 .155 .327
Constant -1.734 .362 23.014 1 .000 .177
a Variable(s) entered on step 1: RACE3, RACE1SM, RACE3SM.

NOTE: Values for Other: 

LOGISTIC REGRESSION VAR=low
  /METHOD=ENTER race1 race2 race1sm race2sm smoke.

Case Processing Summary
Unweighted Cases(b) N Percent
Selected Cases(a) Included in Analysis 189 100.0
Missing Cases 0 .0
Total 189 100.0
Unselected Cases 0 .0
Total 189 100.0
a The variable RACE1 is constant for all selected cases. Since a constant was requested in the model, it will be removed from the analysis.
b If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 0 < 2500g .00 130 0 100.0
1.00 59 0 .0
Overall Percentage

68.8
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 -.790 .157 25.327 1 .000 .454

Variables not in the Equation(a)

Score df Sig.
Step 0 Variables RACE2 1.727 1 .189
RACE1SM 4.924 1 .026
RACE2SM 4.074 1 .044
SMOKE 4.924 1 .026
a Residual Chi-Squares are not computed because of redundancies.

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 6.993 3 .072
Block 6.993 3 .072
Model 6.993 3 .072

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 227.679 .036 .051


Classification Table(a)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 1 < 2500g .00 126 4 96.9
1.00 53 6 10.2
Overall Percentage

69.8
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) RACE2 .351 .588 .356 1 .551 1.420
RACE1SM .629 .349 3.248 1 .072 1.875
RACE2SM .565 .911 .385 1 .535 1.760
Constant -1.139 .235 23.606 1 .000 .320
a Variable(s) entered on step 1: RACE2, RACE1SM, RACE2SM.

page 84 Table 3.20 Estimated logistic regression coefficients for the variable smoke, log-likelihood, the likelihood ratio test statistic (G), and the resulting p-value for estimation of the stratified odds ratio and assessment of homogeneity of odds ratios across strata defined by race. 

LOGISTIC REGRESSION VAR=low
  /METHOD=ENTER smoke.

Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 189 100.0
Missing Cases 0 .0
Total 189 100.0
Unselected Cases 0 .0
Total 189 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 0 < 2500g .00 130 0 100.0
1.00 59 0 .0
Overall Percentage

68.8
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 -.790 .157 25.327 1 .000 .454

Variables not in the Equation

Score df Sig.
Step 0 Variables SMOKE 4.924 1 .026
Overall Statistics 4.924 1 .026

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 4.867 1 .027
Block 4.867 1 .027
Model 4.867 1 .027

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 229.805 .025 .036


Classification Table(a)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 1 < 2500g .00 130 0 100.0
1.00 59 0 .0
Overall Percentage

68.8
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) SMOKE .704 .320 4.852 1 .028 2.022
Constant -1.087 .215 25.627 1 .000 .337
a Variable(s) entered on step 1: SMOKE.
  
LOGISTIC REGRESSION VAR=low
  /METHOD=ENTER smoke race2 race3.

Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 189 100.0
Missing Cases 0 .0
Total 189 100.0
Unselected Cases 0 .0
Total 189 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 0 < 2500g .00 130 0 100.0
1.00 59 0 .0
Overall Percentage

68.8
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 -.790 .157 25.327 1 .000 .454

Variables not in the Equation

Score df Sig.
Step 0 Variables SMOKE 4.924 1 .026
RACE2 1.727 1 .189
RACE3 1.797 1 .180
Overall Statistics 14.127 3 .003

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 14.697 3 .002
Block 14.697 3 .002
Model 14.697 3 .002

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 219.975 .075 .105


Classification Table(a)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 1 < 2500g .00 119 11 91.5
1.00 48 11 18.6
Overall Percentage

68.8
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) SMOKE 1.116 .369 9.135 1 .003 3.052
RACE2 1.084 .490 4.894 1 .027 2.956
RACE3 1.108 .400 7.668 1 .006 3.030
Constant -1.840 .353 27.205 1 .000 .159
a Variable(s) entered on step 1: SMOKE, RACE2, RACE3. 
LOGISTIC REGRESSION VAR=low
  /METHOD=ENTER smoke race2 race3 race2sm race3sm.

Case Processing Summary
Unweighted Cases(a) N Percent
Selected Cases Included in Analysis 189 100.0
Missing Cases 0 .0
Total 189 100.0
Unselected Cases 0 .0
Total 189 100.0
a If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value Internal Value
.00 0
1.00 1


Classification Table(a,b)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 0 < 2500g .00 130 0 100.0
1.00 59 0 .0
Overall Percentage

68.8
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 -.790 .157 25.327 1 .000 .454

Variables not in the Equation

Score df Sig.
Step 0 Variables SMOKE 4.924 1 .026
RACE2 1.727 1 .189
RACE3 1.797 1 .180
RACE2SM 4.074 1 .044
RACE3SM .652 1 .420
Overall Statistics 15.865 5 .007

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 17.854 5 .003
Block 17.854 5 .003
Model 17.854 5 .003

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 216.818 .090 .127


Classification Table(a)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 1 < 2500g .00 126 4 96.9
1.00 53 6 10.2
Overall Percentage

69.8
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) SMOKE 1.750 .598 8.561 1 .003 5.757
RACE2 1.514 .752 4.051 1 .044 4.545
RACE3 1.743 .595 8.592 1 .003 5.714
RACE2SM -.557 1.032 .291 1 .590 .573
RACE3SM -1.527 .883 2.993 1 .084 .217
Constant -2.303 .524 19.280 1 .000 .100
a Variable(s) entered on step 1: SMOKE, RACE2, RACE3, RACE2SM, RACE3SM.

page 86 Figure 3.4 Graph of the estimated logit of low birth weight and 95 percent confidence intervals as a function of weight at the last menstrual period for white women.

NOTE: This graph cannot be reproduced in SPSS.

page 87 Figure 3.5 Graph of the estimated probability of low weight birth and 95 percent confidence intervals as a function of weight at the last menstrual period for white women.

NOTE: This graph cannot be reproduced in SPSS.

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