### 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