We will use the generalized linear model function `glm()`

to estimate a logistic regression-remember that we have a dummy dependent variable. The function is very similar to the `lm()`

function- the only difference is that there is an additional argument called `family()`

. The `family()`

function will tell R that we want to estimate a logistic regression.

Letâ€™s see it in practice, all we have to do is to include the following line in the `glm()`

function:

`family = binomial(link = "logit") argument`

```
logit.model<-glm(incumbent~ sociotropic_pros+egocentric_retro+left_right, data=eco_voting,family = binomial(link = "logit"))
summary(logit.model)
```

```
##
## Call:
## glm(formula = incumbent ~ sociotropic_pros + egocentric_retro +
## left_right, family = binomial(link = "logit"), data = eco_voting)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.7153 -0.7594 -0.3541 0.7221 2.9429
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -5.88946 0.49714 -11.847 < 2e-16 ***
## sociotropic_pros 0.29030 0.10063 2.885 0.00392 **
## egocentric_retro 0.23379 0.10793 2.166 0.03030 *
## left_right 0.79782 0.06612 12.067 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1042.32 on 793 degrees of freedom
## Residual deviance: 742.53 on 790 degrees of freedom
## (479 observations deleted due to missingness)
## AIC: 750.53
##
## Number of Fisher Scoring iterations: 5
```

Interpreting the results of a logistic regression model is not the same as the interpretation of the linear model. Remember that for the linear model the coefficient describe the effect of a unit change (increase or decrease) in X on Y.

For the logistic regression the interpretation of the coefficient is: a one unit change (increase or decrease) in X is associated with a \(\hat{\beta}\) change in the log-odds of the dependent variable (Y), holding all other variables constant.

For example, the coefficient describing perceptions about the economy `sociotropic_pros`

is equal to \(0.047\), implying that the log-odds of voting for the party in government are \(0.047\) higher when the respondent believe that the economy is doing well, holding all other variables constant.