### Let’s load a dataset first

I will be using the birthwt dataset which can be found in the MASS library:

``````library(MASS)
data(birthwt)
``````

It is very important to make sure that any categorical variable is coded as factor:

``````birthwt\$race = as.factor(birthwt\$race)
birthwt\$smoke = as.factor(birthwt\$smoke)
birthwt\$ht = as.factor(birthwt\$ht)
birthwt\$ui = as.factor(birthwt\$ui)
``````

### Now we can run a logistic regression model

``````model = glm(low ~ age + race + smoke + ht + ui + lwt, data = birthwt, family = "binomial")
summary(model)
``````
``````Call:
glm(formula = low ~ age + race + smoke + ht + ui + lwt, family = "binomial",
data = birthwt)

Deviance Residuals:
Min       1Q   Median       3Q      Max
-1.7323  -0.8328  -0.5345   0.9868   2.1673

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)  0.437240   1.191931   0.367  0.71374
age         -0.018256   0.035354  -0.516  0.60559
race2        1.280641   0.526695   2.431  0.01504 *
race3        0.901880   0.434362   2.076  0.03786 *
smoke1       1.027571   0.393931   2.609  0.00909 **
ht1          1.857617   0.688848   2.697  0.00700 **
ui1          0.895387   0.448494   1.996  0.04589 *
lwt         -0.016285   0.006859  -2.374  0.01758 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 234.67  on 188  degrees of freedom
Residual deviance: 203.95  on 181  degrees of freedom
AIC: 219.95

Number of Fisher Scoring iterations: 4
``````

The output for the coefficients is quite intuitive to understand. A closer look at the last part of the summary is necessary though:

``````    Null deviance: 234.67  on 188  degrees of freedom
Residual deviance: 203.95  on 181  degrees of freedom
AIC: 219.95
``````

This compares the deviance values for two models: one with no predictor and another one with all the predictors. Using the difference in variance (234.67 - 203.95) and the difference in parameters (188 - 181) we can look up the probability that the model with all predictors is better than the model with no predictors in a Chi square table.