SPSS Textbook Examples
Applied Logistic Regression, Second Edition, by Hosmer and Lemeshow
Chapter 2: Multiple Logistic Regression

page 32 Table 2.1 An example of the coding of the design variables for race, coded at three levels. 

get file='lowbwt.sav'.

recode race (2=1) (else=0) into race2.
recode race (3=1) (else=0) into race3.
execute.

list race race2 race3
 / cases=from 1 to 3.

     RACE    RACE2    RACE3

     2.00     1.00      .00
     3.00      .00     1.00
     1.00      .00      .00

Number of cases read:  3    Number of cases listed:  3

page 36 Table 2.2 Estimated coefficients for a multiple logistic regression model using the variables age, weight at last menstrual period (lwt), race and number of first trimester physician visits from the low birth weight study. 

LOGISTIC REGRESSION VAR=low
  /METHOD=ENTER age lwt race2 race3 ftv
  /PRINT=SUMMARY.
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 AGE 2.674 1 .102
LWT 5.438 1 .020
RACE2 1.727 1 .189
RACE3 1.797 1 .180
FTV .749 1 .387
Overall Statistics 11.388 5 .044

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 12.099 5 .033
Block 12.099 5 .033
Model 12.099 5 .033

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 222.573 .062 .087


Classification Table(a)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 1 < 2500g .00 125 5 96.2
1.00 54 5 8.5
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) AGE -.024 .034 .499 1 .480 .976
LWT -.014 .007 4.741 1 .029 .986
RACE2 1.004 .498 4.066 1 .044 2.729
RACE3 .433 .362 1.430 1 .232 1.542
FTV -.049 .167 .087 1 .768 .952
Constant 1.295 1.071 1.461 1 .227 3.651
a Variable(s) entered on step 1: AGE, LWT, RACE2, RACE3, FTV.

page 38 Table 2.3 Estimated coefficients for a multiple logistic regression model using the variables lwt and race from the low birth weight study. 

LOGISTIC REGRESSION VAR=low
  /METHOD=ENTER lwt 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 LWT 5.438 1 .020
RACE2 1.727 1 .189
RACE3 1.797 1 .180
Overall Statistics 10.757 3 .013

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 11.413 3 .010
Block 11.413 3 .010
Model 11.413 3 .010

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 223.259 .059 .082


Classification Table(a)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 1 < 2500g .00 124 6 95.4
1.00 53 6 10.2
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) LWT -.015 .006 5.587 1 .018 .985
RACE2 1.081 .488 4.906 1 .027 2.948
RACE3 .481 .357 1.816 1 .178 1.617
Constant .805 .845 .908 1 .341 2.238
a Variable(s) entered on step 1: LWT, RACE2, RACE3.

page 42 Table 2.4 Estimated covariance matrix of the estimated coefficients in Table 2.3. 

LOGISTIC REGRESSION VAR=low
  /METHOD=ENTER lwt race2 race3
  /PRINT=SUMMARY 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 LWT 5.438 1 .020
RACE2 1.727 1 .189
RACE3 1.797 1 .180
Overall Statistics 10.757 3 .013

Omnibus Tests of Model Coefficients

Chi-square df Sig.
Step 1 Step 11.413 3 .010
Block 11.413 3 .010
Model 11.413 3 .010

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 223.259 .059 .082


Classification Table(a)

Predicted
< 2500g Percentage Correct

Observed .00 1.00
Step 1 < 2500g .00 124 6 95.4
1.00 53 6 10.2
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) LWT -.015 .006 5.587 1 .018 .985
RACE2 1.081 .488 4.906 1 .027 2.948
RACE3 .481 .357 1.816 1 .178 1.617
Constant .805 .845 .908 1 .341 2.238
a Variable(s) entered on step 1: LWT, RACE2, RACE3.

Correlation Matrix

Constant LWT RACE2 RACE3
Step 1 Constant 1.000 -.958 .055 -.343
LWT -.958 1.000 -.206 .155
RACE2 .055 -.206 1.000 .306
RACE3 -.343 .155 .306 1.000

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

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

lwt/lwt: (.006)**2 = .00036 
lwt/race2: (.006)*(.488)*(-.206) = -.000603168 
lwt/race3: (.006)*(.357)*(.155) = .00033201 
lwt/constant: (.006)*(.845)*(-.958) = -.00485706 
race2/race2: (.488)*2 = .238144 
race2/race3: (.488)*(.357)*(.306) = .053310096 
race2/constant: (.488)*(.845)*(.055) = .0226798 
race3/race3: (.357)**2 = .127449 
race3/constant: (.357)*(.845)*(-.343) = -.103471095 
constant/constant: (.845)**2 = .714025