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SPSS Textbook Examples
Applied Logistic Regression, Second Edition, by Hosmer and Lemeshow
Chapter 1: Introduction to the Logistic Regression Model

page 3 Table 1.1 Age and coronary heart disease (CHD) status of 100 subjects. 

Get file='chdage.sav'.

compute agrp=age.
recode agrp (20 thru 29=1)(30 thru 34=2)(35 thru 39=3)(40 thru 44=4)(45 thru 49=5)(50 thru 54=6)(55 thru 59=7)(60 thru 69=8).
execute.

list id age agrp chd.


       ID       AGE     AGRP       CHD

     1.00     20.00     1.00       .00
     2.00     23.00     1.00       .00
     3.00     24.00     1.00       .00
     4.00     25.00     1.00       .00
     5.00     25.00     1.00      1.00
     6.00     26.00     1.00       .00
     7.00     26.00     1.00       .00
     8.00     28.00     1.00       .00
     9.00     28.00     1.00       .00
    10.00     29.00     1.00       .00
    11.00     30.00     2.00       .00
    12.00     30.00     2.00       .00
    13.00     30.00     2.00       .00
    14.00     30.00     2.00       .00
    15.00     30.00     2.00       .00
    16.00     30.00     2.00      1.00
    17.00     32.00     2.00       .00
    18.00     32.00     2.00       .00
    19.00     33.00     2.00       .00
    20.00     33.00     2.00       .00
    21.00     34.00     2.00       .00
    22.00     34.00     2.00       .00
    23.00     34.00     2.00      1.00
    24.00     34.00     2.00       .00
    25.00     34.00     2.00       .00
    26.00     35.00     3.00       .00
    27.00     35.00     3.00       .00
    28.00     36.00     3.00       .00
    29.00     36.00     3.00      1.00
    30.00     36.00     3.00       .00
    31.00     37.00     3.00       .00
    32.00     37.00     3.00      1.00
    33.00     37.00     3.00       .00
    34.00     38.00     3.00       .00
    35.00     38.00     3.00       .00
    36.00     39.00     3.00       .00
    37.00     39.00     3.00      1.00
    38.00     40.00     4.00       .00
    39.00     40.00     4.00      1.00
    40.00     41.00     4.00       .00
    41.00     41.00     4.00       .00
    42.00     42.00     4.00       .00
    43.00     42.00     4.00       .00
    44.00     42.00     4.00       .00
    45.00     42.00     4.00      1.00
    46.00     43.00     4.00       .00
    47.00     43.00     4.00       .00
    48.00     43.00     4.00      1.00
    49.00     44.00     4.00       .00
    50.00     44.00     4.00       .00

       ID       AGE     AGRP       CHD

    51.00     44.00     4.00      1.00
    52.00     44.00     4.00      1.00
    53.00     45.00     5.00       .00
    54.00     45.00     5.00      1.00
    55.00     46.00     5.00       .00
    56.00     46.00     5.00      1.00
    57.00     47.00     5.00       .00
    58.00     47.00     5.00       .00
    59.00     47.00     5.00      1.00
    60.00     48.00     5.00       .00
    61.00     48.00     5.00      1.00
    62.00     48.00     5.00      1.00
    63.00     49.00     5.00       .00
    64.00     49.00     5.00       .00
    65.00     49.00     5.00      1.00
    66.00     50.00     6.00       .00
    67.00     50.00     6.00      1.00
    68.00     51.00     6.00       .00
    69.00     52.00     6.00       .00
    70.00     52.00     6.00      1.00
    71.00     53.00     6.00      1.00
    72.00     53.00     6.00      1.00
    73.00     54.00     6.00      1.00
    74.00     55.00     7.00       .00
    75.00     55.00     7.00      1.00
    76.00     55.00     7.00      1.00
    77.00     56.00     7.00      1.00
    78.00     56.00     7.00      1.00
    79.00     56.00     7.00      1.00
    80.00     57.00     7.00       .00
    81.00     57.00     7.00       .00
    82.00     57.00     7.00      1.00
    83.00     57.00     7.00      1.00
    84.00     57.00     7.00      1.00
    85.00     57.00     7.00      1.00
    86.00     58.00     7.00       .00
    87.00     58.00     7.00      1.00
    88.00     58.00     7.00      1.00
    89.00     59.00     7.00      1.00
    90.00     59.00     7.00      1.00
    91.00     60.00     8.00       .00
    92.00     60.00     8.00      1.00
    93.00     61.00     8.00      1.00
    94.00     62.00     8.00      1.00
    95.00     62.00     8.00      1.00
    96.00     63.00     8.00      1.00
    97.00     64.00     8.00       .00
    98.00     64.00     8.00      1.00
    99.00     65.00     8.00      1.00
   100.00     69.00     8.00      1.00

Number of cases read:  100    Number of cases listed:  100

page 4 Figure 1.1 Scatterplot of CHD by AGE for 100 subjects. 

IGRAPH
 /X1 = VAR(age)
 /Y = VAR(chd)
 /SCATTER COINCIDENT = NONE.
Interactive Graph

page 4 Table 1.2 Frequency table of age group by CHD. 

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

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


AGRP * CHD Crosstabulation
Count

CHD Total
.00 1.00
AGRP 1.00 9 1 10
2.00 13 2 15
3.00 9 3 12
4.00 10 5 15
5.00 7 6 13
6.00 3 5 8
7.00 4 13 17
8.00 2 8 10
Total 57 43 100
 

page 5 Figure 1.2 Plot of the percentage of subjects with CHD in each age group.

NOTE: agrp was used to make this graph instead of age as in the text. 

aggregate outfile='table12.sav'
  / break=agrp / totn=n(chd)
  / present=sum(chd).
execute.

get file='table12.sav'.

compute prop=present/totn.

IGRAPH
 /X1 = VAR(agrp)
 /Y = VAR(prop)
 /SCATTER COINCIDENT = NONE.

  Interactive Graph

page 10 Table 1.3 Results of fitting the logistic regression model to the data in Table 1.1. 

get file='chdage.sav'.

LOGISTIC REGRESSION VAR=chd
  /METHOD=ENTER age.
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 AGE 26.399 1 .000
Overall Statistics 26.399 1 .000

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 29.310 1 .000
Block 29.310 1 .000
Model 29.310 1 .000

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 107.353 .254 .341


Classification Table(a)

Predicted
CHD Percentage Correct

Observed .00 1.00
Step 1 CHD .00 45 12 78.9
1.00 14 29 67.4
Overall Percentage

74.0
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) AGE .111 .024 21.254 1 .000 1.117
Constant -5.309 1.134 21.935 1 .000 .005
a Variable(s) entered on step 1: AGE.

page 20 Table 1.4 Estimated covariance matrix of the estimated coefficients in Table 1.3. 

LOGISTIC REGRESSION VAR=chd
  /METHOD=ENTER age
  /PRINT=SUMMARY corr.
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 AGE 26.399 1 .000
Overall Statistics 26.399 1 .000

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 29.310 1 .000
Block 29.310 1 .000
Model 29.310 1 .000

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 107.353 .254 .341


Classification Table(a)

Predicted
CHD Percentage Correct

Observed .00 1.00
Step 1 CHD .00 45 12 78.9
1.00 14 29 67.4
Overall Percentage

74.0
a The cut value is .500

Variables in the Equation

B S.E. Wald df Sig. Exp(B)
Step 1(a) AGE .111 .024 21.254 1 .000 1.117
Constant -5.309 1.134 21.935 1 .000 .005
a Variable(s) entered on step 1: AGE.

Correlation Matrix

Constant AGE
Step 1 Constant 1.000 -.978
AGE -.978 1.000

NOTE: for the variances: var=(se)**2. 

NOTE: for the covariances: cov=corr*se*se.

age/age: (.024)**2 = .000579
constant/constant: (1.134)**2 = 1.218517
age/constant: (-.978)*(.024)*(1.134) = -0.026677

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