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### Logistic Regression with SPSS

#### LOGISTIC REGRESSION Procedure

Unlike in SAS, the SPSS procedure LOGISTIC REGRESSION models the probability of Y=1 or Y's higher sorted value. Suppose the response variable Y is 0 or 1 binary (This is not a limitation for SPSS either. The values can be either numeric or character as long as they are dichotomous), and X1 and X2 are two regressors of interest. To run a logistic regression, use:

```  logistic regression var=y with x1 x2.
```
Example 9: SPSS Logistic Regression in LOGISTIC REGRESSION procedure (individual data)

Using the data in Example 1, you can use:

```  logistic regression var=s with t.
```

You will have the SPSS output:

```                    L O G I S T I C    R E G R E S S I O N

Total number of cases:      387 (Unweighted)
Number of selected cases:   387
Number of unselected cases: 0

Number of selected cases:                 387
Number rejected because of missing data:  0
Number of cases included in the analysis: 387

Dependent Variable Encoding:

Original       Internal
Value          Value
.00       0
1.00       1

Dependent Variable..   S

Beginning Block Number  0.  Initial Log Likelihood Function

-2 Log Likelihood   106.98843

* Constant is included in the model.

Beginning Block Number  1.  Method: Enter

Variable(s) Entered on Step Number
1..       T

Estimation terminated at iteration number 6 because
Log Likelihood decreased by less than .01 percent.

-2 Log Likelihood       95.375
Goodness of Fit        346.446

Chi-Square    df Significance

Model Chi-Square        11.614     1        .0007
Improvement             11.614     1        .0007

Classification Table for S
Predicted
.00    1.00     Percent Correct
0  I    1
Observed        +-------+-------+
.00      0   I    0  I   12  I     .00%
+-------+-------+
1.00     1   I    0  I  375  I  100.00%
+-------+-------+
Overall  96.90%

---------------------- Variables in the Equation -----------------------

Variable           B      S.E.     Wald    df      Sig       R    Exp(B)

T             -.0807     .0224  13.0289     1    .0003  -.3211     .9225
Constant      5.4152     .7275  55.4000     1    .0000
```

The output shows that the estimated logit is

where p is the probability of having an ingot ready for rolling. This is the same result as with the use of the DESCENDING option in SAS PROC LOGISTIC.

#### PROBIT Procedure

You can also use the SPSS PROBIT procedure to fit a logistic regression. The PROBIT procedure supports the model with grouped data. To fit a logistic regression, use:

```  probit r of n with x1 x2
/model logit.
```

where R represents the response count and N represents the observation count.

Example 10: SPSS Logistic Regression in PROBIT procedure (grouped data)

Using the same data in Example 1, you can use the following syntax. Notice that N=1 must be generated for all the observations because the number of trials is 1 for this individual data set.

```
compute n = 1.
execute.
probit r of n with t
/model logit
/print none.
```

The resulting SPSS output will be:

```* * * * * * * * * * * *  P R O B I T    A N A L Y S I S  * * * * * * * * * * * *

Parameter estimates converged after 16 iterations.
Optimal solution found.

Parameter Estimates (LOGIT model:  (LOG(p/(1-p))) = Intercept + BX):

Regression Coeff.  Standard Error     Coeff./S.E.

T                 -.08070          .02236        -3.60965

Intercept  Standard Error  Intercept/S.E.

5.41524          .72755         7.44314

Pearson  Goodness-of-Fit  Chi Square =    346.453    DF = 385   P =  .921

Since Goodness-of-Fit Chi square is NOT significant, no heterogeneity
factor is used in the calculation of confidence limits.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
```

Next: Probit Regression
Prev: Logistic Regression with SAS
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